Browse Function problems Studdy Solved!

Problem 2201

(1 point) Suppose that $f(x)=x^{1 / 3}(x+3)^{2 / 3}$ (A) Find all critical values of $f$ if there are no critical values, enter None. If there are more than one, enter them separated by commas Critical value(s) $=-3,-1,0$ (B) Use interval notation to indicate where $f(x)$ is increasing
Note: When using interval notation in WeBWork, you use Ifor $\infty,-1$ for $-\infty$ , and $\mathbf{U}$ for the union symbol. If there are no values that satisfy the required condition, then enter " 0 " without the quotation marks Increasing $(-3,-1) U(0, I)$ (C) Use interval notation to indicate where $f(x)$ is decreasing
Decreasing $\square$ (D) Find the $x$ -coordinates of all local maxima of $f$ If there are no local maxima, enter None If there are more than one, enter them separated by commas
Local maxima at $x=-1$ $\square$ (E) Find the $x$ -coordinates of all local minima of $f$ If there are no local minima, enter None If there are more than one, enter them separated by commas
Local minima at $x=0$ $\square$ (F) Use interval notation to indicate where $f(x)$ is concave up
Concave up $\square$ (G) Use interval notation to indicate where $f(x)$ is concave down.
Concave down: $\square$ (H) Find all inflection points of $f$ . If there are no inflection points, enter None. If there are more than one, enter them separated by commas Inflection point(s) at $x=$ $\square$ (I) Use all of the preceding information to sketch a graph of $f$ When you're finished, enter a 1 in the box below
Graph Complete $\square$

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Problem 2202

ina owelagar
Travail sur la fonction rationnelle BB Rappel : Si tu n'es pas sûr d'une réponse, tu as le droit de me poser une question... Tu fais ton travail sur une feuille PROPRE et tu COMMUNIQUES ta démarche. Le but premier de ce travail est de te rendre apte à travailler la fonction rationnelle. Je t'encourage à valider tes réponses avec Desmos, mais les démarches algébriques sont obligatoires. Numéro 1. A) Fais l'étude complète de la fonction rationnelle suivante $f(x)=\frac{104 x-1204}{8 x-96}$
L'étude complète veut dire : 1) Déterminer la règle sous la forme $f(x)=\frac{a}{x-h}+k$ $f(x)=\frac{\frac{11}{2}}{x-12}+13$ 2) Représentation graphique, avec les asymptotes $\rightarrow \rightarrow \rightarrow$ 3) Domaine $\qquad$ Codomaine $y \in\{B\}$ $\qquad$ 4) Abscisse à l'origine et ordonnée à l'origine (AVEC CALCULS) $x=12$ $\begin{aligned} f(x) & =\frac{\frac{11}{2}}{0-12}+13 \\ & =\frac{301}{24} \end{aligned}$ $0=\frac{\frac{11}{2}}{x^{-12}}+13$ $\begin{array}{rr} 0=\frac{11}{\frac{2}{x-12}}+13 & -13 x+156=\frac{11}{2} \\ -13=\frac{11}{\frac{11}{x-12}} & \frac{-13 x}{}=-\frac{301}{2} \\ & \\ & x=\frac{301}{26} \\ & \end{array}$ 5) La variation $\frac{\text { decrorssanle } 1\{12\}}{\{-12}$ 6) Le signe $\qquad$ Pasitive xe 700 Il n'eralle pas! 7) Les extrémung B) Détermine l'intervalle pour lequel $f(x) \leq 21$ . AVEC CALCULS...
RÉPONSE: $\qquad$

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Problem 2203

3. Suppose production function is given by $f(k, l)=k^{\frac{2}{3}} l^{\frac{2}{3}}$ , then the elasticity of substitution is (a) 2 (b) 1 (c) $\frac{4}{3}$ (d) 0

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Problem 2204

Evaluate the triple integral $\iiint_{E} x y d V$ where $E$ is the solid tetrahedon with vertices $(0,0,0),(7,0,0),(0,2,0),(0,0,5)$ .

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Problem 2205

A balloon rises vertically from the ground 200 m away from an observer. It rises with a position function $h=50 t^{2}$ where $h$ is the height of the balloon in metres and $t$ is in seconds. How fast is the angle of elevation changing 2 seconds after the balloon leaves the ground?

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Problem 2206

Use the figures to calculate the left and right Riemann sums for $f$ on the given interval and the given value of $n$ . $f(x)=\frac{1}{x}+3 \text { on }[1,5] ; n=4$
The left Riemann sum for $f$ is 14.08 . (Round to two decimal places as needed.) The right Riemann sum for $f$ is (Round to two decimal places as needed.)

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Problem 2207

8. The function $f(x)=-x e^{x}+2$ is concave down at $x=0$ . a. Find the tangent line of $f$ at $x=0$ . b. What is the estimate for $f(-0.1)$ using the local linear approximation for $f$ at $x=0$ ? c. Is it an underestimate or overestimate? Explain.

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Problem 2208

```latex \textbf{Practice Q\#2: Determine if the given scenarios are linear relations AND functions.}
\begin{enumerate} \item A campsite in a Provincial park charges \ $35 for the car + driver, then \$15 per additional person. \\ Linear$ (y / n) $: \qquad Function$ (y / n) : \qquad Reason: \item A population of fruit flies doubles every 12 hours. \\ Linear (y / n) $: \qquad Function$ (y / n) : \qquad Reason: \item Linear (y / n) $: \qquad y \\ Function$ (y / n) : \qquad Reason: \item \begin{tabular}{|c|c|c|c|c|} \hline s(\mathrm{~km} / \mathrm{h}) & 50 & 60 & 70 & 80 \\ \hline d(\mathrm{~m}) & 13 & 20 & 27 & 35 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|} \hline t(\min ) & 0 & 2 & 4 & 6 \\ \hline a(m)$ & 12000 & 11600 & 11200 & 10800 \\ \hline \end{tabular} \end{enumerate}
\textbf{Practice Q\#3: Determine the rate of change for each segment of Kat's ocean dive.}
\begin{tabular}{|c|c|} \hline Segment & Rate of Change \\ \hline OA & \\ \hline AB & \\ \hline BC & \\ \hline CD & \\ \hline DE & \\ \hline \end{tabular} ```

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Problem 2209

Question 2, 7.1.79 Part 1 of 3 HW Score: $5.88 \%, 1$ of 17 points Points: 0 of 1 Save
The function models the number of accidents, $f(x)$ , per 50 million miles driven as a function of a driver's age, $x$ , in years, where $x$ includes drivers from ages 16 through 74 , inclusive. The graph of $f$ is shown. Find and interpret $f(69)$ . Identify this information as a point on the graph of $f$ .
Find $\mathrm{f}(69)$ . $f(69)=$ $\square$ (Simplify your answer. Type an integer or a decimal.)

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Problem 2210

Let $R=[0,4] \times[-1,2]$ . Create a Riemann sum by subdividing $[0,4]$ into $m=2$ intervals, and $[-1,2]$ into $n=3$ subintervals, then use it to estimate the value of $\iint_{R}\left(4-x y^{2}\right) d A$
Take the sample points to be the upper left corner of each rectangle.
Answer: 28

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Problem 2211

Solve using the quadratic formula and find the zeros $f(x)=(x-1)\left(x^{2}-x+1\right)$

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Problem 2212

The function $f(x)$ is a cubic function and the zeros of $f(x)$ are $-1,5$ and 6 . Assume the leading coefficient of $f(x)$ is 1 . Write the equation of the cubic polynomial in standard form.

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Problem 2213

7. $f(x)=x^{4}+x^{3}+7 x-1: f(-3)$
8. $f(x)=2 x^{4}-18 x^{2}+7 ; f(2)$
9. A bicycle manufacturer determines that the profit per bicycle when producing $x$ bicycles per day is $\boldsymbol{P}(\boldsymbol{x})=-\boldsymbol{x}^{4}+7 \boldsymbol{x}^{3}-5 x^{2}+x$ . Use the Remainder Theorem to find the profit per bicycle when four bicycles are produced each day.
10. The value $V$ (in dollars) of a signed baseball card can be modeled by the function $V(t)=2 t^{3}-48 t^{2}+300 t$ where $t$ is the number of years since 1980. Use the Remainder Theorem to find the value of the card in 2025.

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Problem 2214

Name: Date: Topic: Class:

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Problem 2215

The atmospheric pressure on an object decreases as altitude increases. If $a$ is the height (in km) above sea level, then the pressure $P(a)$ (in mmHg) is approximated by $P(a)=760 e^{-0.13 a}$ . (a) Find the atmospheric pressure at sea level. (b) Determine the atmospheric pressure at 5.304 km (the altitude of Mount Foraker). Round to the nearest whole unit. Do not round intermediate calculations.

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Problem 2216

13. The function $f$ given by $f(x)=x^{3}+12 x-24$ is A. increasing for $x<-2$ , decreasing for $-2<x<2$ , increasing for $x>2$ B. decreasing for $x<0$ , increasing for $x>0$ C. increasing for all $x$ D. decreasing for all $x$ E. decreasing for $x<-2$ , increasing for $-2<x<2$ , decreasing for $x>2$

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Problem 2217

(a) $f(x)=\frac{6}{x}, x \neq 0$ $\begin{array}{l} g(x)=\frac{6}{x}, x \neq 0 \\ f(g(x))=\square \\ g(f(x))=\square \end{array}$ $f$ and $g$ are inverses of each other $f$ and $g$ are not inverses of each other (b) $f(x)=x+4$ $\begin{array}{l} g(x)=-x+4 \\ f(g(x))=\square \\ g(f(x))=\square \end{array}$ $f$ and $g$ are inverses of each other $f$ and $g$ are not inverses of each othe

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Problem 2218

Question Watch Video Show Examples
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. $y=88(0.977)^{x}$
Answer Attempt 1 out of 2
Growth $\square$ \% increase Submit Answer

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Problem 2219

Question Watch Video Show Examples
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. $y=45(1.82)^{x}$
Answer Attempt 1 out of 2
Growth $\square$ \% increase Submit Answer

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Problem 2220

What is the slope of line d? ¿Cuál es la pendiente de la recta d? -3 /
4
2 Fill in the Blank 1 point What is the $y$ - intercept of the graph in question 1? ¿Cuál es la intersección y de la gráfica de la pregunta 1?
3

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Problem 2221

Suppose that the functions $f$ and $g$ are defined as follows. $\begin{array}{l} f(x) = -3x + 5 \\ g(x) = \sqrt{2x - 3} \end{array}$
Find $f \cdot g$ and $f+g$ . Then, give their domains using interval notation.
$(f \cdot g)(x) = (-3x + 5)(\sqrt{2x - 3})$
Domain of $f \cdot g: \left[\frac{3}{2}, \infty\right)$
$(f+g)(x) =$ $\square$
Domain of $f+g$ : $\square$

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Problem 2222

Find the area of the region bound by the following equations: $y=6 x+6, \quad y=0, \quad x=3 \text { and } x=7$

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Problem 2223

The function $f$ is given by $f(x)=5 \cdot(0.7)^{x}$ . Which of the following describes $f$ ?
A The function $f$ models exponential decay and $\lim _{x \rightarrow \infty} f(x)=0$ . (B) The function $f$ models exponential decay and $\lim _{x \rightarrow \infty} f(x)=\infty$ . (C) The function $f$ models exponential growth and $\lim _{x \rightarrow \infty} f(x)=0$ . (D) The function $f$ models exponential growth and $\lim _{x \rightarrow \infty} f(x)=\infty$ .

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Problem 2224

The function $m$ is given by $m(x)=36^{(x / 2)}$ . Which of the following expressions could also define $m(x)$ ? (A) $6^{z}$ (B) $6 \cdot 6^{x}$ (C) $18^{x}$ (D) $18 \cdot 36^{2}$

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Problem 2225

The function $f$ is given by $f(x)=2^{x}$ , and the function $g$ is given by $g(x)=\frac{f(z)}{8}$ . For which of the following transformations is the graph of $g$ the image of the graph of $f$ ? A) A horizontal translation to the left 3 units (B) A horizontal translation to the right 3 units (C) A vertical translation up $\frac{1}{8}$ unit (D) A vertical translation down $\frac{1}{8}$ unit

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Problem 2226

Use the information provided to write the factored form equation of each parabola. zeros: $(3,0),(5,0)$ , Passes through: $(4,1)$ Find the 'a' value: $\square$
Type in the entire function using the format: $y=a(x-p)(x-q)$ with no spaces. $\square$

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Problem 2227

The figure shows a portion of the graph of a function $f$ . Which of the following conclusions is possible for f? (A) $f$ is a quadratic function because the output values are proportional over equal-length input-value intervals. (B) $f$ is a quadratic function because the average rates of change over consecutive equallength input-value intervals can be given by a linear function. (C) $f$ is an exponential function because the output values are proportional over equallength input-value intervals. (D) $f$ is an exponential funotion because the average rates of change over consecutive equal-ength inpusvalue intervals can be given by a linear function.

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Problem 2228

Write the quadratic function in standard form. $y=4(x-3)(x-5)$
Find the values of $\mathrm{a}, \mathrm{b}$ , and c for the function $y=a x^{2}+b x+c$ .
What is the value of $a$ ? $\square$
What is the value of $b$ ? $\square$
What is the value of $c$ ? $\square$

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Problem 2229

The value, in millions of dollars, of transactions processed by an online payment platform is modeled by the function $M$ . The value is expected to increase by $6.1 \%$ each quarter of a year. At time $t=0$ years, 54 million dollars of transactions were processed. If $t$ is measured in years, which of the following is an expression for $M(t)$ ? (Note: A quarter is one fourth of a year.) (A) $54(0.061)^{(i / 4)}$ (B) $54(0.061)^{(4 t)}$ (C) $54(1.061)^{(t / 4)}$ (D) $54(1.061)^{(4)}$

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Problem 2230

Use the Trapezoidal Rule to approximate $\int_{-0.8}^{0.6} \frac{\tan x}{x+3} \mathrm{~d} x$ using $n=3$ (Round your answer to 4 decimal places.) $\int_{-0.8}^{0.6} \frac{\tan x}{x+3} d x \approx$ $\square$

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Problem 2231

Drow Graph of function for: $\begin{array}{l} f(x)=1 / 3 x^{2}-2 / 3 x-5 \\ \text { vertex: }\left(1,-\frac{16}{3}\right) \text { or }(1,-5,3) \\ y \text { - intercept: }(0,-5) \\ x \text { - intercepts: }(5,0) \text { and }(-3,0) \end{array}$

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Problem 2232

lodine-131 has a half-life of 8 days. In a particular sample, the amount of iodine-131 remaining after $d$ days can be modeled by the function $h$ given by $h(d)=A_{0}(0.5)^{(d / 8)}$ , where $A_{0}$ is the amount of iodine-131 in the sample at time $d=0$ . Which of the following functions $k$ models the amount of iodine- 131 remaining after $t$ hours, where $A_{0}$ is the amount of iodine- 131 in the sample at time $t=0$ ? (There are 24 hours in a day. $\cdot$ ot $t=24 d$ .) (A) $k(t)=A_{0}(0.5)^{(t / 24)}$ (B) $k(t)=A_{0}\left(0.5^{(1 / 24)}\right)^{(8 t)}$ (C) $k(t)=A_{0}\left(0.5^{(24)}\right)^{(4 / 8)}$ (D) $k(t)=A 0\left(0.5^{(1 / 1 m 2)}\right)^{t}$

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Problem 2233

The figure shows the graph of an exponential decay function $f$ . The coordinates of two of the points are Iabeled. If $y=f(x)$ , what is the ycoordinate of the point on the graph where $x=0$ ? (A) 40 (B) 30 (C) 20 (D) 15

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Problem 2234

The amount of carbon 14 remaining in a sample that originally contained $A$ grams is given by $C(t)=A(0.999879)^{t}$ where $t$ is time in years. How old, to the nearest 1,000 years, is a fossil in which only $33 \%$ of the carbon 14 has decayed? $\square$ yr

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Problem 2235

Which of the following statements is true about the exponential function $h$ given by $h(x)=-3 \cdot 4^{2} ?$ (A) $h$ is always increasing, and the graph of $h$ is always concave up (B) $h$ is always increasing, and the graph of $h$ is always concave down. (C) $h$ is always decreasing, and the graph of $h i s$ always concave up. (D) $h$ is always decreasing, and the graph of $h$ is always concave down.

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Problem 2236

Graph the given function by making a table of coordinates. $f(x)=4^{x}$
Complete the table of coordinates. \begin{tabular}{|c|c|c|c|c|c|} \hline $\mathbf{x}$ & -2 & -1 & 0 & 1 & 2 \\ \hline $\mathbf{y}$ & $\square$ & $\square$ & $\square$ & $\square$ & $\square$ \\ \hline \end{tabular} (Type integers or fractions. Simplify your answers.)

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Problem 2237

Suppose that the functions $f$ and $g$ are defined as follows. $\begin{array}{l} f(x)=4 x-5 \\ g(x)=\sqrt{5 x+1} \end{array}$
Find $f \cdot g$ and $f-g$ . Then, give their domains using interval notation. $(f \cdot g)(x)=$ $\square$
Domain of $f \cdot g$ : $\square$ $(f-g)(x)=$ $\square$
Domain of $f-g$ : $\square$

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Problem 2238

Which transformation is needed to graph the function $g(x)=4^{-x}$ ? Choose the correct answer below. A. The graph of $f(x)=4^{x}$ should be reflected about the $y$ -axis. B. The graph of $f(x)=4^{x}$ should be reflected about the x -axis. C. The graph of $\mathrm{f}(\mathrm{x})=4^{\mathrm{x}}$ should be horizontally stretched by a factor of -1 . D. The graph of $f(x)=4^{x}$ should be vertically stretched by a factor of -1 .

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Problem 2239

$\equiv 1$ 2 $\equiv 3$ $=4$ $\equiv 5$ $=6$ 7 8 9 10 11 12
For the functions $f(x)=\frac{3}{x+4}$ and $g(x)=\frac{5}{x-1}$ , find the composition $f \circ g$ and simplify your answer as much as possible. Write the domain using interval notation. $(f \circ g)(x)=$ $\square$
Domain of $f \circ g$ : $\square$

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Problem 2240

Example: Write an algorithm, that reads a character, then will determine whether it is VOWEL letter or not. Note: Vowel letters are: A, E, I, O, U.

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Problem 2241

$\lim _{x \rightarrow 0} \frac{x^{3}-1}{\ln x}$

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Problem 2242

If $y=\sin \left(x^{2}\right)$ , what is $\frac{d y}{d x}$ using the chain rule? - I. $2 x \cos \left(x^{2}\right)$ - II. $2 x \sin \left(x^{2}\right)$ - III. $\cos \left(x^{2}\right)$ - IV. $2 x \sin (x)$ A. IV B. I C. III D. II

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Problem 2243

If $F(x)=\left\{\begin{array}{lll}-3 x & x<-1 & \text { find }(a) f(-2)(b) f(-1)(c) f(c)\end{array}\right.$ (a) $-3(-2)=6$ (b) 0 (c) $2(0)^{2}+1=1$ What is the Domain

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Problem 2244

2. The total stopping distance $T$ of a vehicle is $T=2.5 x+0.5 x^{2}$ where $T$ is in feet and $x$ is the speed in miles-per-hour. Approximate the change and percent change in the total stopping distance as the speed changes from $x=25$ to $x=26 \mathrm{mph}$ .

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Problem 2245

Die Eìnführung der Rippenqualle Beroe ovata, einem Fressfeind, konnte die Population im Schwarzen Meer zurückdrängen. Die Funktion g mit $g(x)=30+x^{2} \cdot e^{-0,1 \cdot x}, 0 \leq x \leq 80$ modelliert die Populationsdichte mit Fressfeind. Die folgenden Aufgaben beziehen sich alle auf die Funktion g. e) Berechnen Sie die maximale Anzahl an Mnemiopsis leidyi pro Kubikmeter. f) Berechnen Sie den Zeitpunkt, zu dem die Population an stärksten abnimmt. 3 g) Bestimmen Sie die durchschnittliche Änderungsrate im Zeitintervall [20; 80]. Untersuchen Sie, ob es einen Zeitpunkt in diesem Zeitintervall gibt, an dem die momentane Änderungsrate so groß ist wie die durchschnittliche Änderungsrate des Zeitintervalls. 4 5
Eine vereinfachte Modellierung geht davon aus, dass die Populationsdichte ab einem bestimmten Zeitpunkt $z$ durch die Tangente an den Graphen von $g$ im Punkt $P(z \mid g(z))$ beschrieben werden kann. h) Bestimmen Sie für $z=70$ die Gleichung der Tangente und den Zeitpunkt, zu dem die Populationsdichte nach diesem vereinfachten Modell null ist. 5

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Problem 2246

Graphing with Intercept Form Graph the function. Label the vertex and the $\boldsymbol{x}$ -intercepts.
44. $y=(x-3)(x-5)$
45. $y=-(x+2)(x-2)$
46. $y=(x+1)(x$
47. $y=-2(x-1)(x-2)$
48. $y=\frac{1}{2}(x+4)(x-2)$
49. $y=\frac{1}{3}(x-3)($
50. $y=3(x+3)(x-1)$
51. $y=4(x-7)(x+2)$
52. $y=x(x-5)$

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Problem 2247

The derivative of $\sqrt{\sin 2 x}$ is
Select one: $\frac{\cos x}{\sqrt{\sin x}}$ $-\frac{\cos 2 x}{\sqrt{\sin 2 x}}$ $\frac{\cos 2 x}{\sqrt{\sin 2 x}}$ $\frac{\cos 2 x}{2 \sqrt{\sin 2 x}}$ Check

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Problem 2248

3. Soit g la fonction définie sur $\left[1 ;+\infty\left[\right.\right.$ par: $\quad g(x)=x^{3}-3 x-3$ . a) Montrer que la fonction $g$ admet une fonction réciproque définie sur un intervalle $J$ à déterminer. b) Montrer que l'équation $g(x)=0$ admet une unique solution $\alpha$ dans $[1 ;+\infty[$ . c) Montrer que $\left(g^{-1}\right)^{\prime}(0)=\frac{1}{3\left(\alpha^{2}-1\right)}$ .

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Problem 2249

2. (1,0 ponto cada item) Usando as regras de diferenciaçāo, encontre as derivadas das funçöes a seguir, simplificando ao máximo se possível. (a) $y=\frac{\operatorname{sen} x}{\cos x-1}$ (c) $y=\cos \left(2^{x}\right)$ (b) $f(x)=x \operatorname{arctg} x-\frac{1}{2} \ln \left(1+x^{2}\right)$ (d) $y=(x)^{(\cosh x)}$

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Problem 2250

1. Kurvendiskussion
Gegeben ist die Funktion $f(x)=(x-1) \cdot e^{x}$ . a) Bestimmen Sie die Ableitungen $\mathrm{f}^{\prime}, \mathrm{f}^{\prime \prime}$ und $\mathrm{f}^{\prime \prime \prime}$ . b) Untersuchen Sie die Funktion f auf Nullstellen. c) Die Funktion f besitzt ein Extremum und einen Wendepunkt. Wo liegen diese Punkte? d) Untersuchen Sie das Verhalten von f für $\mathrm{x} \rightarrow-\infty$ bzw. $\mathrm{x} \rightarrow \infty$ mit einer Tabelle. e) Skizzieren Sie den Graphen von $\mathrm{f}(-3 \leq \mathrm{x} \leq 2)$ .

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Problem 2251

$f(x)=-2 x^{2}-8 x-4$
Does the function have a minimum or maximum value? Minimum Maximum
What is the function's minimum or maximum value? $\square$ Where does the minimum or maximum value occur? $x=-12$

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Problem 2252

Consider the function. $f(x)=|x-2|+5$
Which two statements about the graph of the function are true? For $x<2$ , the graph is decreasing, but for $x>2$ the graph is increasing. For $x<2$ , the graph is increasing, but for $x>2$ the graph is decreasing. The function has a maximum at $(2,5)$ . The function has a maximum at $(5,2)$ . The function has a minimum at $(2,5)$ .

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Problem 2253

inis is the graph of a linear function.
What are the domain and the range of the function?
Domain: Range:

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Problem 2254

What are the domain and the range of the function?
Domain: $\square$ Range: $\square$

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Problem 2255

What are the domain and the range of the function?
Domain: $\square$ Range:

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Problem 2256

18. A ball is thrown into the air follows the quadratic function $h(t)=-8 t^{2}+16 t$ , where the time $t$ is measured in seconds and $h(t)$ , measured in feet, is the height above ground level. a) What is the independent variable? b) What is the dependent variable? c) At what time the ball will reach its maximum height? d) What is the maximum height the ball will reach? e) What are the coordinates of the vertex? f) What are the coordinates of $y$ -intercept? g) What are the coordinates of $x$ -intercept(s)? h) What is the axis of symmetry of function $h(t)$ ? i) Is function $h(t)$ even, odd, or neither and why?

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Problem 2257

Escribe la fórmula explicita en forma de función. Write the explicit formula in function form. $\begin{array}{l} a_{n}=5+0.2(n-1) \\ f(n)= \end{array}$
Parte B Cuál es el punto de corte con el eje y de la función? What is the $y$ -intercept of the function? $\square$ $\square$

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Problem 2258

2 \begin{tabular}{|c|c|} \hline \multicolumn{2}{|l|}{\begin{tabular}{l} obsenvala tabla \\ Consider the fable \end{tabular}} \\ \hline \multicolumn{2}{|c|}{Table N} \\ \hline $16$ & ( \\ \hline ( -2 & 10 \\ \hline -1 & 6 \\ \hline 0 & 4 \\ \hline 1 & 2 \\ \hline \end{tabular}
Explica por que la Table N no representa una función lineal Explain why Table $N$ does not represents a linear function. 星

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Problem 2259

19. A ball is thrown into the air follows the quadratic function $h(t)=-5 t^{2}+19 t+20$ , where the time $t$ is measured in seconds and $h(t)$ , measured in feet, is the height above ground level. a) What is the independent variable? b) What is the dependent variable? c) At what time the ball will reach its maximum height? d) What is the maximum height the ball will reach? e) What are the coordinates of the vertex? f) What are the coordinates of $y$ -intercept? g) What are the coordinates of $x$ -intercept(s)? h) What is the axis of symmetry of function $h(t)$ ? i) Is function $h(t)$ even, odd, or neither and why?

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Problem 2260

Which is equivalent to $\log _{2} 17=4 ?$ $\log n=\frac{\log 2}{4}$ $n=\frac{\log 2}{\log 4}$ $17=\log 4 \cdot \log 2$ $\log n=4 \log 2$

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Problem 2261

Find $P(-2)$ for the polynomial $P(x) = 2x^3 - 4x^2 - 15$ using synthetic substitution.

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Problem 2262

de usar para dar respuesta a los ejercicios. Ejercicio sin procedımientu a) Conociendo que el $\operatorname{Csc}(\alpha)=\frac{8 \sqrt{49}}{49}$ con $\alpha \in$ IIIC, calcula las razones trigonométricas directas.

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Problem 2263

7-18 Use la parte 1 del teorema fundamental del cálculo para encontrar la derivada de cada una de las siguientes funciones.
7. $g(x)=\int_{1}^{x} \frac{1}{t^{3}+1} d t$
8. $g(x)=\int_{3}^{x} e^{t^{2}-t} d t$

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Problem 2264

7. $g(x)=\int_{1}^{x} \frac{1}{t^{3}+1} d t$

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Problem 2265

b) Conociendo que el $\operatorname{Sen}(\propto)=\frac{\sqrt{27}}{21}$ con $\propto \in$ IVC, calcula las razones trigonométricas inversas.

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Problem 2266

13. $h(x)=\int_{1}^{e^{x}} \ln t d t$

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Problem 2267

14. $h(x)=\int_{1}^{\sqrt{x}} \frac{z^{2}}{z^{4}+1} d z$

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Problem 2268

b) Conociendo que el $\operatorname{Sen}(\propto)=\frac{\sqrt{27}}{21}$ con $\propto \in \mathrm{IVC}$ , calcula las razones trigonométricas inversas.

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Problem 2269

$q(x)=2 x+6+\left(x^{2}-9\right)$

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Problem 2270

Find $f(-1), f(0)$ and $f(1)$ for the following function. $f(x)=-2 x$ $f(-1)=$ $\square$ $f(0)=$ $\square$ $f(1)=$ $\square$

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Problem 2271

Which statements are true? Select all that apply. A. The amplitude of $y=2 \sin \left(\frac{1}{2} x\right)$ is $\frac{1}{2}$ B. The period of $y=2 \sin \left(\frac{1}{2} x\right)$ is $\pi$ . C. The amplitude of $y=2 \sin \left(\frac{1}{2} x\right)$ is $\frac{\pi}{2}$ . D. The period of $y=2 \sin \left(\frac{1}{2} x\right)$ is $4 \pi$ . E. The period of $y=2 \sin \left(\frac{1}{2} x\right)$ is $\frac{1}{2}$ F. The amplitude of $y=2 \sin \left(\frac{1}{2} x\right)$ is 2

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Problem 2272

Find $y^{\prime}$ . $\begin{array}{l} y=\left(\frac{x+1}{x-7}\right)^{7} \\ y^{\prime}=\square \end{array}$

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Problem 2273

Given $g(x)=-3 x+4$ , find $g(1)$

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Problem 2274

$f(x)=4 x^{2}+|-9 x|$
Choose the correct answer. Odd Even Neither

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Problem 2275

Find the minimum value of the parabola $y=x^{2}+8$ .
Simplify your answer and write it as a proper fraction, improper fraction, or integer. $\square$ Submit

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Problem 2276

What is the first derivative of $f(x)=\log _{2}\left(6 x^{3}+2 x+6\right) ?$
Select the correct answer below: $\log _{2}\left(18 x^{2}+2\right)$ $\frac{1}{(\ln 2)\left(6 x^{3}+2 x+6\right)}$ $\frac{18 x^{2}+2}{(\ln 2)\left(6 x^{3}+2 x+6\right)}$ $\frac{(\ln 2)\left(18 x^{2}+2\right)}{6 x^{3}+2 x+6}$ $\frac{18 x^{2}+2}{6 x^{3}+2 x+6}$

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Problem 2277

Find the $y$ -intercept of the parabola $y=4 x^{2}+2 x+4$
Simplify your answer and write it as a proper fraction, improper fraction, or integer. $\square$ Submit

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Problem 2278

If $r(x)=\log _{5}\left(\frac{x^{6} 5^{x}}{5 x^{2}+5}\right)$ , find $r^{\prime}(x)$
Select the correct answer below: $r^{\prime}(x)=\frac{6}{x \ln 5}+1-\frac{10 x}{\left(5 x^{2}+5\right) \ln 5}$ $r^{\prime}(x)=\frac{5 x^{2}+5}{x^{5}(5) \ln 5}$ $r^{\prime}(x)=\frac{6}{x \ln 5}+\frac{x 5^{x-1}}{5^{2} \ln 5}-\frac{10 x}{\left(5 x^{2}+5\right) \ln 5}$ $r^{\prime}(x)=\frac{6}{x}+1-\frac{10 x}{5 x^{2}+5}$

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Problem 2279

La hauteur de l'eau dans un port est de $\mathbf{2 1} \mathbf{m}$ à marée haute et de 11 m à marée basse. La marée termine un cycle environ toutes les 12 h . a) Formule une équation correspondant à la hauteur des eaux par rapport au temps $t$ , en heures, après la marée basse. La marée basse a eu lieu à 14 h . b) Trace le graphiqse de la fonction sur une période de 48 h après la marée basse, laquelle a eu lieu à 14 h . c) Indique les heures où l'eau atteint sa hauteur: i) maximale ii) minimale iii) moyenne d) Fais une estimation de la hauteur de l'eau: i) à 17 h ii) à 21 h e) Fais une estimation des heures où l'eau atteint : i) 14 m ii) 20 m iii) au moins 18 m .

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Problem 2280

What is $g^{\prime}(x)$ when $g(x)=\ln \left(3 x^{3}+2\right)$ ?
Select the correct answer below: $\ln \left(9 x^{2}\right)$ $\frac{1}{3 x^{3}+2}$ $\frac{3 x^{3}+2}{9 x^{2}}$ $\frac{9 x^{2}}{\ln \left(3 x^{3}+2\right)}$ $\frac{9 x^{2}}{3 x^{3}+2}$

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Problem 2281

What is the first derivative of $t(x)=\ln \left(4 x^{3}+4 x^{2}+6 x+4\right)$ ?
Select the correct answer below: $\frac{1}{4 x^{3}+4 x^{2}+6 x+4}$ $\frac{12 x^{2}+8 x+6}{4 x^{3}+4 x^{2}+6 x+4}$ $\frac{12 x^{2}+8 x+6}{\ln \left(4 x^{3}+4 x^{2}+6 x+4\right)}$ $\ln \left(12 x^{2}+8 x+6\right)$ $\frac{4 x^{3}+4 x^{2}+6 x+4}{12 x^{2}+8 x+6}$

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Problem 2282

5. a) Determine the equation in vertex form of a function that has a range of $(-\infty, 14]$ and $x$ -intercepts at -5 and 1. (3 marks)

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Problem 2283

Graph all vertical and horizontal asymptotes of the rational function $f(x)=\frac{-6 x-13}{4 x-6}$

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Problem 2284

$P(n)$ , given below, is the price in dollars for $n$ grams of vitamins. $P(n)=0.25 n+5.2$
Complete the following statements.
Let $P^{-1}$ be the inverse function of $P$ . Take $x$ to be an output of the function $P$ . That is, $x=P(n)$ and $n=P^{-1}(x)$ . (a) Which statement best describes $P^{-1}(x)$ ? The amount of vitamins (in grams) for a price of $x$ dollars. The price (in dollars) for $x$ grams of vitamins. The ratio of the price (in dollars) to the number of grams, $x$ . The reciprocal of the price (in dollars) for $x$ grams of vitamins. (b) $P^{-1}(x)=\frac{x-5.2}{.25}$ (c) $P^{-1}(8.5)=$ $\square$

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Problem 2285

Stuffco Industries makes model airplanes and wants to know their average cost and revenue at a production level of 300 . If their cost function is $C(x)=2700+65 x+x^{2}$ and their revenue function is $R(x)=530 x-x^{2}$ , what is their average cost and revenue?
Select the correct answer below: Average cost: $\$ 274 ;$ Average Revenue: $\$ 530$ . Average cost: $\$ 380$ ; Average Revenue: $\$ 250$ . Average cost: $\$ 374$ ; Average Revenue: $\$ 230$ . Average cost: $\$ 112,200 ;$ Average Revenue: $\$ 69,000$

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Problem 2286

What translation of $y=x^{2}$ results in a new function with vertex $(-3,6) ?$ 3 units left and 6 units up 3 units right and 6 units down 6 units right and 3 units down 6 units left and 3 units up

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Problem 2287

Graph the function. $f(x)=-2 x^{2}+3$
Plot five points on the graph of the function: one point with $x=0$ , two points with negative $x$ -values, and two points with positive $x$ -values. Then click on the graph-a-function button.

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Problem 2288

Let $f(x)=-5 \ln (\sin x)$
Then $f^{\prime}(x)=$ $\square$ and $f^{\prime \prime}(x)=$ $\square$

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Problem 2289

Question 3 (1 point) If $f(x)=2 \cos 3 x$ , find $f^{\prime}\left(\frac{\pi}{3}\right)$ . a) 3 b) 0 c) -6 d) 6

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Problem 2290

Graph the function. $f(x)=-4 x^{2}+5$
Plot five points on the graph of the function: one point with $x=0$ , two points with negative $x$ -values, and two points with positive $x$ -values. Then click on the graph-a-function button.

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Problem 2291

For the following function, a) determine whether it is one-to-one; b) if it is one-to-one, find its inverse function. $f(x)=x+5$
Is the given function a one-to-one function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. Yes, the function is one-to-one. The inverse function is $\mathrm{f}^{-1}(\mathrm{x})=$ $\square$ (Simplify your answer.) B. No, the the function is not one-to-one.

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Problem 2292

Pictured to the right is the that follow. a. Identify the zeros of the graph of $g(x)$ and their multiplicities. Explain specifically how you know the multiplicity of each zero. $x=-3$ , mult of 3 ; because it sways across the $x$ -axis. $x=2$ , mult of 2 , becouse it bounces on the $x$ -axis. b. Will the leading coefficient of the equation be positive or negative? Give a reason for your answer based on the end behaviors and the degree of the function.

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Problem 2293

For Problems 12 and 13, consider the table below \begin{tabular}{|c|c|c|c|c|} \hline $x$ & $f(x)$ & $f^{\prime}(x)$ & $g(x)$ & $g^{\prime}(x)$ \\ \hline 1 & 2 & $\frac{1}{2}$ & -3 & 5 \\ \hline 2 & 3 & 1 & 0 & 4 \\ \hline 3 & 4 & 2 & 2 & 3 \\ \hline 4 & 6 & 4 & 3 & $\frac{1}{2}$ \\ \hline \end{tabular}
12. If $h(x)=f^{-1}(x)$ find $h^{\prime}(3)$
13. If $h(x)=g^{-1}(x)$ find $h^{\prime}(-3)$

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Problem 2294

What is the first derivative of $q(x)=\left(4^{x}\right)^{5} ?$
Select the correct answer below: $q^{\prime}(x)=4^{5 x}(5 \ln 4)$ $q^{\prime}(x)=5\left(4^{x}\right)^{4}$ $q^{\prime}(x)=5\left(4^{5 x}\right)$ 人to $q^{\prime}(x)=(5 x) 4^{5 x-1}$ $q^{\prime}(x)=4^{5 x}(4 \ln 5)$

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Problem 2295

Name MP2T2B Mathematics Department Jenlsha Thempson, AP(S) $11 / 20 / 2024$ Score $\qquad$ Questions 1-13 are 6 points each. Questions 14 is 8 points and question 15 is 14 points. MCs21X - AP Calculus BC Ms. M. E. Dela Cruz
1. Using a GC, find, correct to 3 decimal places, an estimate for the value of $x$ at which the graph of $y=x^{4}-2 x^{3}+5 x-8$ has a horizontal tangent. $y^{\prime}=4 x^{3}-6 x^{2}+5$
2. Which is true about the function $f(x)=\sqrt[3]{x^{2}}$ ? (A) It has a vertical tangent at $\mathrm{x}=0$ . (B) It has a stationary point at $x=0$ . (D) It has a cusp at $x=0$ . (C) It has a relative maximum at $x=0$ . (E) It is discontinuous at $x=0$ .
3. If $y=\frac{x}{x^{2}+4}$ , then $\frac{d y}{d x}=$ (A) $\frac{x^{2}-4}{\left(x^{2}+4\right)^{2}}$ (B) $\frac{4-x^{2}}{\left(x^{2}+4\right)^{2}}$ $(1)\left(x^{2}+4\right)+(x)(2 x)$ $(x-4)+(x-1)$
4. Which of the following functiche (D) $\frac{4-x^{2}}{x^{2}+4}$ (E) $\frac{x^{2}-4}{x^{2}+4}$ (A) $y=x^{3}$ (B) $y=\frac{1}{x+1}$ (C) $y=|x|$ (D) $y=\sqrt{x}$ (E) $y=(x-2)^{\frac{2}{3}}$
5. If $f$ is continuous on $[a, b]$ which of the following is always true? (A) $\quad f$ is differentiable on $(a, b)$ . (B) $\quad f$ is either increasing or decreasing on [a, b] (C) $f$ has both a maximum and a minimum value on [a, b]. (D) The maximum value of $f$ is greater than the minimum value of $f$ .
6. Find all the intervals over which the function $f(x)=x^{3}-3 x^{2}$ is (a) increasing $(6, \infty)$ $3 x^{2}-6 x$ 6 $3 x\left(x^{2}-6\right) \quad x=6$ (b) decreasing $(-\infty, 0) \cup(0,6)$
7. Write, in point-slope form, the equation of the tangent line to the graph of $y=x-x^{2}$ at $(1,0)$ .
8. Find the slope-intercept form of the equation of the normal line to the curve $y=x^{3}$ at the point at which $x=\frac{1}{3}$ .
9. Find the exact values of the absolute extrema of the function $f(x)=\frac{x^{3}}{x+2}$ on $[-1,1]$

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Problem 2296

If $t$ is in minutes since the drug was administered, the concentration, $C(t) \mathrm{in} \mathrm{ng} / \mathrm{ml}$ , of a drug in a patient's bloodstream is given by $C(t)=20 t e^{-0.04 t}$ . (a) How long does it take for the drug to reach peak concentration? What is the peak concentration?
Round your answers to one decimal place.
The drug reaches its peak concentration at i $\square$ minutes.
The peak concentration is i $\square$ $\mathrm{ng} / \mathrm{ml}$ . (b) What is the concentration of the drug in the body after 15 minutes? After an hour?
Round your answers to one decimal place. The concentration after 15 minutes is $\square$ $\mathrm{ng} / \mathrm{ml}$ .
The concentration after 60 minutes is $\square$ i $\mathrm{ng} / \mathrm{ml}$ . (c) If the minimum effective concentration is $10 \mathrm{ng} / \mathrm{ml}$ , when should the next dose be administered? cytosolic proteins cytoso

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Problem 2297

$f(x)=\ln \left((3 x)\left(5^{2 x}\right)\right)$

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Problem 2298

Level $3 / 4$ the sale of $x$ villograms of coflee can be modelled by the fintion $P(x)=\frac{4 x-200}{x+400}$ a) Sketch a graph of this function. 7) c) If 500 kg of coffee is sold, determine the profit. d) Determine the $x$ -intercept. What does this value represent?

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Problem 2299

7. $y=\frac{x^{2}+1}{x}$ a. Find intervals increasing or decreasing
6. find intervaler concave up or concave down c. find all arymptoter d. points at local max, local min, paI e.sketch the function

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Problem 2300

The numbers in the table follow a linear pattern. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 2 & 13 \\ \hline 4 & 23 \\ \hline 6 & 33 \\ \hline 9 & 48 \\ \hline 12 & 63 \\ \hline 15 & $?$ \\ \hline \end{tabular}
What is the missing $y$ value? A 80 B 90 C 75 D 78

See Solution

Function

Problem 2201

Problem 2202

Problem 2203

3. Suppose production function is given by f(k,l)=k23l23f(k, l)=k^{\frac{2}{3}} l^{\frac{2}{3}}f(k,l)=k32​l32​, then the elasticity of substitution is (a) 2 (b) 1 (c) 43\frac{4}{3}34​ (d) 0

Problem 2204

Evaluate the triple integral ∭ExydV\iiint_{E} x y d V∭E​xydV where EEE is the solid tetrahedon with vertices (0,0,0),(7,0,0),(0,2,0),(0,0,5)(0,0,0),(7,0,0),(0,2,0),(0,0,5)(0,0,0),(7,0,0),(0,2,0),(0,0,5).

Problem 2205

A balloon rises vertically from the ground 200 m away from an observer. It rises with a position function h=50t2h=50 t^{2}h=50t2 where hhh is the height of the balloon in metres and ttt is in seconds. How fast is the angle of elevation changing 2 seconds after the balloon leaves the ground?

Problem 2206

Problem 2207

8. The function f(x)=−xex+2f(x)=-x e^{x}+2f(x)=−xex+2 is concave down at x=0x=0x=0. a. Find the tangent line of fff at x=0x=0x=0. b. What is the estimate for f(−0.1)f(-0.1)f(−0.1) using the local linear approximation for fff at x=0x=0x=0 ? c. Is it an underestimate or overestimate? Explain.

Problem 2208

Problem 2209

Problem 2210

Problem 2211

Solve using the quadratic formula and find the zeros f(x)=(x−1)(x2−x+1)f(x)=(x-1)\left(x^{2}-x+1\right)f(x)=(x−1)(x2−x+1)

Problem 2212

The function f(x)f(x)f(x) is a cubic function and the zeros of f(x)f(x)f(x) are −1,5-1,5−1,5 and 6 . Assume the leading coefficient of f(x)f(x)f(x) is 1 . Write the equation of the cubic polynomial in standard form.

Problem 2213

Problem 2214

Name: Date: Topic: Class:

Problem 2215

Problem 2216

Problem 2217

Problem 2218

Problem 2219

Question Watch Video Show ExamplesGiven the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=45(1.82)xy=45(1.82)^{x}y=45(1.82)xAnswer Attempt 1 out of 2Growth □\square□ \% increase Submit Answer

Problem 2220

What is the slope of line d? ¿Cuál es la pendiente de la recta d? -3 /42 Fill in the Blank 1 point What is the yyy - intercept of the graph in question 1? ¿Cuál es la intersección y de la gráfica de la pregunta 1?3

Problem 2221

Problem 2222

Find the area of the region bound by the following equations: y=6x+6,y=0,x=3 and x=7y=6 x+6, \quad y=0, \quad x=3 \text { and } x=7y=6x+6,y=0,x=3 and x=7

Problem 2223

Problem 2224

The function mmm is given by m(x)=36(x/2)m(x)=36^{(x / 2)}m(x)=36(x/2). Which of the following expressions could also define m(x)m(x)m(x) ? (A) 6z6^{z}6z (B) 6⋅6x6 \cdot 6^{x}6⋅6x (C) 18x18^{x}18x (D) 18⋅36218 \cdot 36^{2}18⋅362

Problem 2225

Problem 2226

Problem 2227

Problem 2228

Problem 2229

Problem 2230

Problem 2231

Problem 2232

Problem 2233

The figure shows the graph of an exponential decay function fff. The coordinates of two of the points are Iabeled. If y=f(x)y=f(x)y=f(x), what is the ycoordinate of the point on the graph where x=0x=0x=0 ? (A) 40 (B) 30 (C) 20 (D) 15

Problem 2234

The amount of carbon 14 remaining in a sample that originally contained AAA grams is given by C(t)=A(0.999879)tC(t)=A(0.999879)^{t}C(t)=A(0.999879)t where ttt is time in years. How old, to the nearest 1,000 years, is a fossil in which only 33%33 \%33% of the carbon 14 has decayed? □\square□ yr

Problem 2235

Problem 2236

Problem 2237

Problem 2238

Problem 2239

Problem 2240

Example: Write an algorithm, that reads a character, then will determine whether it is VOWEL letter or not. Note: Vowel letters are: A, E, I, O, U.

Problem 2241

lim⁡x→0x3−1ln⁡x\lim _{x \rightarrow 0} \frac{x^{3}-1}{\ln x}limx→0​lnxx3−1​

Problem 2242

Problem 2243

Problem 2244

Problem 2245

Problem 2246

Problem 2247

Problem 2248

Problem 2249

Problem 2250

Problem 2251

f(x)=−2x2−8x−4f(x)=-2 x^{2}-8 x-4f(x)=−2x2−8x−4Does the function have a minimum or maximum value? Minimum MaximumWhat is the function's minimum or maximum value? □\square□ Where does the minimum or maximum value occur? x=−12x=-12x=−12

Problem 2252

Problem 2253

inis is the graph of a linear function.What are the domain and the range of the function?Domain: Range:

Problem 2254

What are the domain and the range of the function?Domain: □\square□ Range: □\square□

Problem 2255

What are the domain and the range of the function?Domain: □\square□ Range:

Problem 2256

Problem 2257

Problem 2258

Problem 2259

Problem 2260

3. Suppose production function is given by $f(k, l)=k^{\frac{2}{3}} l^{\frac{2}{3}}$ , then the elasticity of substitution is (a) 2 (b) 1 (c) $\frac{4}{3}$ (d) 0

Evaluate the triple integral $\iiint_{E} x y d V$ where $E$ is the solid tetrahedon with vertices $(0,0,0),(7,0,0),(0,2,0),(0,0,5)$ .

A balloon rises vertically from the ground 200 m away from an observer. It rises with a position function $h=50 t^{2}$ where $h$ is the height of the balloon in metres and $t$ is in seconds. How fast is the angle of elevation changing 2 seconds after the balloon leaves the ground?

8. The function $f(x)=-x e^{x}+2$ is concave down at $x=0$ . a. Find the tangent line of $f$ at $x=0$ . b. What is the estimate for $f(-0.1)$ using the local linear approximation for $f$ at $x=0$ ? c. Is it an underestimate or overestimate? Explain.

Solve using the quadratic formula and find the zeros $f(x)=(x-1)\left(x^{2}-x+1\right)$

The function $f(x)$ is a cubic function and the zeros of $f(x)$ are $-1,5$ and 6 . Assume the leading coefficient of $f(x)$ is 1 . Write the equation of the cubic polynomial in standard form.

Question Watch Video Show Examples
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. $y=45(1.82)^{x}$
Answer Attempt 1 out of 2
Growth $\square$ \% increase Submit Answer

What is the slope of line d? ¿Cuál es la pendiente de la recta d? -3 /
4
2 Fill in the Blank 1 point What is the $y$ - intercept of the graph in question 1? ¿Cuál es la intersección y de la gráfica de la pregunta 1?
3

Find the area of the region bound by the following equations: $y=6 x+6, \quad y=0, \quad x=3 \text { and } x=7$

The function $m$ is given by $m(x)=36^{(x / 2)}$ . Which of the following expressions could also define $m(x)$ ? (A) $6^{z}$ (B) $6 \cdot 6^{x}$ (C) $18^{x}$ (D) $18 \cdot 36^{2}$

The figure shows the graph of an exponential decay function $f$ . The coordinates of two of the points are Iabeled. If $y=f(x)$ , what is the ycoordinate of the point on the graph where $x=0$ ? (A) 40 (B) 30 (C) 20 (D) 15

The amount of carbon 14 remaining in a sample that originally contained $A$ grams is given by $C(t)=A(0.999879)^{t}$ where $t$ is time in years. How old, to the nearest 1,000 years, is a fossil in which only $33 \%$ of the carbon 14 has decayed? $\square$ yr

$\lim _{x \rightarrow 0} \frac{x^{3}-1}{\ln x}$

$f(x)=-2 x^{2}-8 x-4$
Does the function have a minimum or maximum value? Minimum Maximum
What is the function's minimum or maximum value? $\square$ Where does the minimum or maximum value occur? $x=-12$

inis is the graph of a linear function.
What are the domain and the range of the function?
Domain: Range:

What are the domain and the range of the function?
Domain: $\square$ Range: $\square$

What are the domain and the range of the function?
Domain: $\square$ Range:

Which is equivalent to $\log _{2} 17=4 ?$ $\log n=\frac{\log 2}{4}$ $n=\frac{\log 2}{\log 4}$ $17=\log 4 \cdot \log 2$ $\log n=4 \log 2$

Find $P(-2)$ for the polynomial $P(x) = 2x^3 - 4x^2 - 15$ using synthetic substitution.

de usar para dar respuesta a los ejercicios. Ejercicio sin procedımientu a) Conociendo que el $\operatorname{Csc}(\alpha)=\frac{8 \sqrt{49}}{49}$ con $\alpha \in$ IIIC, calcula las razones trigonométricas directas.

7-18 Use la parte 1 del teorema fundamental del cálculo para encontrar la derivada de cada una de las siguientes funciones.
7. $g(x)=\int_{1}^{x} \frac{1}{t^{3}+1} d t$
8. $g(x)=\int_{3}^{x} e^{t^{2}-t} d t$

7. $g(x)=\int_{1}^{x} \frac{1}{t^{3}+1} d t$

b) Conociendo que el $\operatorname{Sen}(\propto)=\frac{\sqrt{27}}{21}$ con $\propto \in$ IVC, calcula las razones trigonométricas inversas.

13. $h(x)=\int_{1}^{e^{x}} \ln t d t$

14. $h(x)=\int_{1}^{\sqrt{x}} \frac{z^{2}}{z^{4}+1} d z$

b) Conociendo que el $\operatorname{Sen}(\propto)=\frac{\sqrt{27}}{21}$ con $\propto \in \mathrm{IVC}$ , calcula las razones trigonométricas inversas.

$q(x)=2 x+6+\left(x^{2}-9\right)$

Find $f(-1), f(0)$ and $f(1)$ for the following function. $f(x)=-2 x$ $f(-1)=$ $\square$ $f(0)=$ $\square$ $f(1)=$ $\square$

Find $y^{\prime}$ . $\begin{array}{l} y=\left(\frac{x+1}{x-7}\right)^{7} \\ y^{\prime}=\square \end{array}$

Given $g(x)=-3 x+4$ , find $g(1)$

$f(x)=4 x^{2}+|-9 x|$
Choose the correct answer. Odd Even Neither