Function

Problem 3401

The monthly revenue $R$ achieved by selling $x$ wristwatches is figured to be $R(x)=75 x-0.2 x^{2}$ . The monthly cost $C$ of selling $x$ wristwatches is $C(x)=30 x+1700$ . (a) How many wristwatches must the firm sell to maximize revenue? What is the maximum revenue? (b) Profit is given as $\mathrm{P}(\mathrm{x})=\mathrm{R}(\mathrm{x})-\mathrm{C}(\mathrm{x})$ . What is the profit function? (c) How many wristwatches must the firm sell to maximize profit? What is the maximum profit? (d) Provide a reasonable explanation as to why the answers found in parts (a) and (c) differ. Explain why a quadratic function is a reasonable model for revenue. (b) The profit function is $\mathrm{P}(\mathrm{x})=45 \mathrm{x}-0.2 \mathrm{x}^{2}-1700$ . (Type an expression using $x$ as the variable.) (c) The firm must sell 113 wristwatches to maximize profit. (Round to the nearest integer as needed.) The maximum profit is $\$ 831.20$ . (Round to two decimal places as needed.) (d) Why do the answer found in part (a) and part (c) differ? Choose the correct answer below. A. The parts differ because part (a) uses the revenue function which is equal to the sum of the profit function and the cost function. B. The parts differ because part (c) uses the profit function which is equal to the product of the revenue function and the cost function. C. The parts differ because part (c) uses the revenue function which is equal to the sum of the profit function and the cost function. D. The parts differ because part (a) uses the profit function which is equal to the difference of the revenue function and the cost function.
Explain why a quadratic function is a reasonable model for revenue. Choose the correct answer below. A. Revenue is the profit of the item times the number $x$ of units actually sold. So the revenue, $R$ , is a quadratic function of the price $p$ . B. Revenue is the profit of the item plus the number $x$ of units actually sold. So the revenue, $R$ , is a quadratic function of the price $p$ . C. Revenue is the selling price of the item times the number $x$ of units actually sold. So the revenue, $R$ , is a quadratic function of the price $p$ . D. Revenue is the selling price of the item plus the number $x$ of units actually sold. So the revenue, $R$ , is a quadratic function of the price $p$ .

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Problem 3402

Identify the linear function from these equations: $f(x)=\frac{3 x+2}{4}$ , $f(x)=\sqrt{x+2}$ , $f(x)=2 x^{2 x-3}$ , $f(x)=\frac{3 x-3}{x^{2}}$ .

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Problem 3403

Sketch the graph of $f(x)=\frac{3}{x+1}+2$ . Include all 6 axis intersections and asymptotes.

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Problem 3404

Identify the equation that represents an absolute value function from these options: $f(x)=-9$ , $f(x)=\frac{1}{3 x}$ , $f(x)=x-3 x^{2}$ , $f(x)=\frac{-1}{4}|x+4|-3$ .

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Problem 3405

Identify the equation that defines a constant function from these options: $f(x)=-\frac{3}{5}$ , $f(x)=3-x$ , $f(x)=9 x$ , $f(x)=\frac{4}{x}$ .

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Problem 3406

Identify the linear function among these equations: $f(x)=5-\frac{3}{x}$ , $f(x)=3x-\frac{2}{5}$ , $f(x)=4x-\frac{5}{2x}$ , $f(x)=|x-4+3|$ .

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Problem 3407

In the expression $\frac{3 g}{4}$ , what does $3 g$ represent in terms of the total gas cost for the trip?

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Problem 3408

An ideal gas has a volume of $1.50 \times 10^{-4} \mathrm{~m}^3$ at $22^{\circ} \mathrm{C}$ and $1.20 \times 10^5$ Pa. Find the temperature in Kelvin when pressure is $2.00 \times 10^5$ Pa.

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Problem 3409

Complete the table using the function $f(x)=\sqrt{x-4}$ . Simplify answers or mark as "Not a real number" if needed.

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Problem 3410

Use the function $f(x)=\sqrt{x-4}$ to find $f(13)$ and $f(85)$ . Simplify answers; note non-real results.

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Problem 3411

Analyze the function $f(x)=|x-3|-1$ : find domain, range, intercepts, increasing/decreasing intervals, and end behavior.

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Problem 3412

Use the function $f(x)=\sqrt{x-4}$ to complete the table. Simplify answers; mark "Not a real number" if needed.

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Problem 3413

Fill in the table using $f(x)=\sqrt{x-4}$ . For $x=0$ , 4, 13, and 85, find $f(x)$ or state "Not a real number".

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Problem 3414

Find values of $x$ not in the domain of $g(x)=\frac{x+5}{x^{2}-4 x-21}$ . List them separated by commas. $x=$

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Problem 3415

Compare the graphs of $g(x)=f(x-2)+7$ and $f(x)$ . Which transformation applies?

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Problem 3416

Compare the graphs of $g(x)=f(x)+5$ and $f(x)$ : Which shift describes $g(x)$ best?

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Problem 3417

جد ارتفاع الجسر عند النقطة التي تبعد 6 م عن بدايته، إذا كانت المسافة بين قاعدتيه 24 م وارتفاعه 9 م.

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Problem 3418

Shift the function $g(x)=4x^{2}-16$ 7 right and 3 down. What is the new equation? A. $h(x)=4(x-9)^{2}-17$ B. $h(x)=4(x+7)^{2}+19$ C. $h(x)=4(x-7)^{2}-19$ D. $h(x)=4(x+9)^{2}-17$

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Problem 3419

Compare the graphs of $f(x)=x^{2}$ and $g(x)=4x^{2}$ . Which statement is true about their relationship?

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Problem 3420

What happens to a function's graph when multiplied by -1? A. Flips over $y=x$ . B. Flips over $y$ -axis. C. Flips over $x$ -axis.

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Problem 3421

Compare $g(x)=\left(\frac{1}{3} x\right)^{2}$ with $f(x)=x^{2}$ . Which transformation describes $g(x)$ ?

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Problem 3422

Compare the graphs of $f(x)=x^{2}$ and $g(x)=4x^{2}$ . Which statement is true about their relationship?

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Problem 3423

What is the new equation when the quadratic function $f(x)=x^{2}$ is shifted right by 12 units? A. $g(x)=x^{2}+12$ B. $g(x)=(x+12)^{2}$ C. $g(x)=x^{2}-12$ D. $g(x)=(x-12)^{2}$

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Problem 3424

Find the new function after shifting $f(x)=x^{2}$ right 1 unit, stretching by 5, and reflecting over the $x$ -axis.

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Problem 3425

What is the equation of the function when the graph of $f(x)=x^{2}$ is flipped over the $x$ -axis? A. $g(x)=-x^{2}$ B. $g(x)=\frac{1}{x^{2}}$ C. $g(x)=x^{-2}$ D. $g(x)=(-x)^{2}$

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Problem 3426

What is the new equation for the function after stretching $f(x)=2^{x}$ vertically by a factor of 3? A. $g(x)=2 \cdot 3^{x}$ B. $g(x)=3 \cdot 2^{x}$ C. $g(x)=2^{3 x}$ D. $g(x)=\frac{1}{3} \cdot 2^{x}$

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Problem 3427

Find the new function from $f(x)=x$ after a vertical stretch by 3 and a flip over the $x$ -axis. A. $g(x)=3 x-1$ B. $g(x)=\frac{3}{x}$ C. $g(x)=-\frac{1}{3} x$ D. $g(x)=-3 x$

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Problem 3428

What is the new function equation after shifting $f(x)=x$ up 6 units? A. $g(x)=\frac{1}{6} x$ B. $g(x)=6 x$ C. $g(x)=x-6$ D. $g(x)=x+6$

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Problem 3429

How does the graph of $f(x)=2^{x}$ change to $g(x)=3 \cdot 2^{x}+5$ ? Select all that apply: A, B, C, D, E.

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Problem 3430

Mrs. Hernandez delivers mail for 41.25 min. After 10 min for 5 houses, how to find remaining houses with $1.25$ min each?

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Problem 3431

Find the chirp count $c$ when the temperature $T=90$ using the formula $T=30+0.28c$ . What does $c$ represent?

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Problem 3432

Mrs. Lopez types words at a rate of 38. Write the equation relating words $w$ and minutes $m$ : $w = 38m$ .

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Problem 3433

Calculate $\cos 48^{\circ}$ and round to two decimal places. Options: A. 0.50 B. 1 C. 0.67 D. 0.48 E. None.

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Problem 3434

Choose the graph of the function $h(x)=\frac{1}{3} x^{2}$ and its parent function.

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Problem 3435

Find the tangent line equation for $f(x)=\sqrt{3-x}$ at a given point.

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Problem 3436

Find the derivative of the function $y=x^{4}+12x$ . What is $\frac{dy}{dx}$ ?

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Problem 3437

What is the value of $\frac{a^{3}-b^{3}}{5}$ for $a=2$ and $b=-3$ ? Options: $-3 \frac{4}{5}$ , $-\frac{3}{5}$ , 3, 7.

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Problem 3438

Find the values of $a$ , $b$ , $c$ , and $d$ in the magic square where rows, columns, and diagonals sum to the same number.

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Problem 3439

Doris hat 42 von 60 Punkten. Hat sie bestanden, wenn sie mindestens $75\%$ benötigt?

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Problem 3440

Simplify $\tan 100^{\circ} + 4 \sin 100^{\circ}$ .

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Problem 3441

Deposit $\$ P$ for 2 years at $8\%$ p.a. Find interest for (i) simple interest and (ii) compound interest. If difference is $\$ 240$ , find $P$ .

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Problem 3442

Identify which of these sets of pairs represents a function: A. $(5,11),(-8,3),(0,7),(0,-6)$ B. $(0,11),(-8,3),(0,7),(-8,-6)$ C. $(11,5),(3,-8),(7,0),(11,-6)$ D. $(5,11),(-8,3),(0,7),(-6,11)$ .

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Problem 3443

Find $\lim _{x \rightarrow \infty} \cos \left(\frac{1+\pi x}{x}\right)$ .

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Problem 3444

Match each trigonometric function with its value:
sin 60° = ?, cos 45° = ?, tan 45° = ?, sec 30° = ?, csc 30° = ?, cot 60° = ?
Choices: $\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}, \frac{2 \sqrt{3}}{3}, 1, \frac{\sqrt{3}}{2}, \frac{\sqrt{3}}{3}, \frac{\sqrt{3}}{2}$

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Problem 3445

Given sides $a=5$ and $b=12$ , find $c$ , $\sin B$ , $\cos B$ , $\tan B$ , and $\sec B$ .

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Problem 3446

Identify the parent function and transformations for: $y=2|x+4|+4$ .

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Problem 3447

Find the value of $\csc 45^{\circ}$ . Simplify your answer with integers or fractions.

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Problem 3448

What does $1+x$ represent in the markup price expression $937(1+x)$ for a computer?

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Problem 3449

Rewrite $\sin 61^{\circ}$ using its cofunction. What is $\sin 61^{\circ}=$ ? (Provide the answer without the degree symbol.)

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Problem 3450

Rewrite $\tan 38^{\circ}$ using its cofunction. What is the simplified answer?

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Problem 3451

Calculate the exact value of $\sec 30^{\circ}$ . Simplify your answer with integers or fractions.

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Problem 3452

Find the exact value of $\sin 60^{\circ}$ . Simplify your answer with radicals, integers, or fractions.

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Problem 3453

Find the exact value of $\tan 30^{\circ}$ . Simplify your answer with integers or fractions.

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Problem 3454

Rewrite $\tan 74^{\circ}$ using its cofunction. What is $\tan 74^{\circ}=$ ? Simplify your answer without the degree symbol.

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Problem 3455

Calculate the exact value of $\csc 45^{\circ}$ . Simplify your answer using integers or fractions.

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Problem 3456

What will a union member's salary be in 9 years if it increases by $5\%$ annually from a current salary of \$87,300?

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Problem 3457

Find the graph of $g(x)=\frac{1}{4} f(x)$ given $f(x)=x^{2}$ .

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Problem 3458

Shift the function $g(x)=4 x^{2}-16$ 9 units right and 1 down. What is the new equation? A. $h(x)=4(x+9)^{2}-17$ B. $h(x)=4(x-17)^{2}-9$ C. $h(x)=4(x-9)^{2}-17$ D. $h(x)=4(x-7)^{2}+16$

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Problem 3459

Find $h(6)$ if $h(x) = x^{2} - 4$ .

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Problem 3460

Find $f(0)$ for the function $f(x)=2x+3$ .

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Problem 3461

Find $f(-4)$ for the function $f(x)=5x-12$ .

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Problem 3462

Complete the table: Input 12 gives Output 48. Rule: Multiply by 4. Find Outputs for Inputs 18, 24, and 30.

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Problem 3463

Find the limit as $x$ approaches 4 for the piecewise function $f(x)$ defined as: $f(x) = -7x + 46$ if $x < 4$ , $12$ if $x = 4$ , $2x^2 - 14$ if $x > 4$ . What is $\lim_{x \rightarrow 4} f(x)$ ?

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Problem 3464

A ball is thrown with a velocity of $41 \mathrm{ft} / \mathrm{s}$ . Its height is $y=41 t-22 t^{2}$ . Find average velocity from $t=2$ and instantaneous velocity at $t=2$ .

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Problem 3465

Find the rate of change of the city's population modeled by $P(t)=22 e^{0.08 t}$ from 2025 to 2034.

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Problem 3466

Graph $f(x)=\frac{|x+2|}{x+2}$ for the range $[-4,4]$ .

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Problem 3467

Find the average rate of change of COVID-19 infections from 0 to 8 days, assuming 0 at day 0. Round to two decimals.

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Problem 3468

Graph $f(x)=\frac{|x+3|}{x+3}$ for $x$ in the range $[-4,4]$ .

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Problem 3469

Find the average rate of change of infections from day 0 to day 16, given $P(0) = 3$ , $P(8) \approx 5.55$ , $P(16) \approx 10.28$ . Round to two decimal places in thousand people per day.

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Problem 3470

How many friends can you invite so that 24 slices of pizza and 90 tokens are evenly shared? How much does each get?

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Problem 3471

Find the $y$ -coordinate of the vertex of the parabola $g$ given points (-1, 1), (3, 9), (4, 6) and $x=2$ .

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Problem 3472

Find the value of $k$ for the quadratic function $y=f(x)$ passing through $(5,1),(7,k),(9,26)$ with average rate change of 1.5.

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Problem 3473

Find $\theta$ using the equation $\cos \theta=\frac{5}{12}$ . Round to the nearest degree if necessary.

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Problem 3474

Encuentra la derivada de $f(x) = 3x^3 - x$ .

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Problem 3475

Calculate the proof of a solution that is 50% ethanol by volume, knowing pure ethanol is 200 proof.

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Problem 3476

Find the number of students in either Chemistry or Physics if there are 91 in Chemistry, 70 in Physics, and 20 in both.

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Problem 3477

In a group of 146 students, 85 speak French and 83 speak Japanese. Find how many speak both languages.

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Problem 3478

Plot several terms of the logistic equation $x_{t+1}=c x_{t}(1-x_{t})$ with $x_{0}=0.4$ and $c=3.5$ .

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Problem 3479

Find the quadratic equation $f(x)$ that matches the points: $(-1, 10)$ , $(0, 14)$ , and $(1, 20)$ .

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Problem 3480

Define the absolute value function $f(x)=|4x+7|$ as a piecewise function.

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Problem 3481

Sello bought $3(x + (2x - 4))$ tickets, where Naomi bought $x$ tickets.

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Problem 3482

Find the rate of change of the city's population, modeled by $P(t)=10 e^{0.04 t}$ , from 2021 to 2030 in thousand persons/year.

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Problem 3483

What transformation changes $f(x)=2|x|-9$ to $g(x)=-2|x|+9$ ?

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Problem 3484

Calculate the average rates of change for COVID-19 infections in Minnesota over these intervals using $\frac{\Delta y}{\Delta x}$ :
1. 0 to 8 days: (calculate)
2. 8 to 16 days: 0.59 thousand/day
3. 0 to 16 days: 0.46 thousand/day

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Problem 3485

What transformation changes $f(x)=2x^{2}+10$ to $g(x)=8x^{2}+10$ ?

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Problem 3486

Identify the transformation that changes $f(x)=3(x-6)^{2}$ into $g(x)=3x^{2}+10$ .

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Problem 3487

Identify the transformation that changes $f(x)=8 x^{2}-8$ to $g(x)=x^{2}-1$ .

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Problem 3488

Identify the transformation that changes $f(x)=10 x^{2}-5$ to $g(x)=2 x^{2}-1$ .

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Problem 3489

Solve for $x$ in the equation $f(x)(1+x)=(1-x)(2+x)$ .

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Problem 3490

Find the average velocity of a ball thrown with $y=41t-22t^{2}$ at $t=2$ for intervals of 0.01, 0.005, 0.002, and 0.001 seconds.

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Problem 3491

Calculate the average rate of change of the function $k(x)=-16 \sqrt{x}$ from $x=12$ to $x=15$ .

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Problem 3492

Determine the domain of the function $h(x)=\frac{1}{\sqrt[4]{x^{2}-3x}}$ .

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Problem 3493

Find the domain of $H(t)=\frac{81-t^{2}}{9-t}$ .

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Problem 3494

Two times the cube of a number minus four: $2x^3 - 4$ .

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Problem 3495

A particle $P$ has a velocity of $v=24-4 t^{2}$ m/s. Find: (a) distance in the first second, (b) when it changes direction, (c) when it returns to start.

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Problem 3496

A particle $P$ moves along a line with displacement $x = \frac{1}{3} t^{3} - 4 t^{2} + 15 t$ . Find: (a) when $P$ is at rest, (b) distance in 5 seconds.

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Problem 3497

Find the distance from the origin when the particle stops, given $v=9t-3t^{2}$ m/s and starts at $t=0$ .

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Problem 3498

Determine if the function represented by the points $(-10, -79)$ , $(-9, -72)$ , $(-8, -65)$ , $(-7, -58)$ , and $(-6, -51)$ is linear, quadratic, cubic, or exponential.

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Problem 3499

Determine the type of function for the points: (5, -1), (6, 6), (7, 25), (8, 62), (9, 123).

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Problem 3500

Determine if the function represented by the points (1, 5), (2, 9), (3, 13), (4, 17), (5, 21) is linear, quadratic, cubic, or exponential.

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1 ...32 33 34 35 36 37 38 ...103

Function

Problem 3401

Problem 3402

Identify the linear function from these equations: f(x)=3x+24f(x)=\frac{3 x+2}{4}f(x)=43x+2​, f(x)=x+2f(x)=\sqrt{x+2}f(x)=x+2​, f(x)=2x2x−3f(x)=2 x^{2 x-3}f(x)=2x2x−3, f(x)=3x−3x2f(x)=\frac{3 x-3}{x^{2}}f(x)=x23x−3​.

Problem 3403

Sketch the graph of f(x)=3x+1+2f(x)=\frac{3}{x+1}+2f(x)=x+13​+2. Include all 6 axis intersections and asymptotes.

Problem 3404

Identify the equation that represents an absolute value function from these options: f(x)=−9f(x)=-9f(x)=−9, f(x)=13xf(x)=\frac{1}{3 x}f(x)=3x1​, f(x)=x−3x2f(x)=x-3 x^{2}f(x)=x−3x2, f(x)=−14∣x+4∣−3f(x)=\frac{-1}{4}|x+4|-3f(x)=4−1​∣x+4∣−3.

Problem 3405

Identify the equation that defines a constant function from these options: f(x)=−35f(x)=-\frac{3}{5}f(x)=−53​, f(x)=3−xf(x)=3-xf(x)=3−x, f(x)=9xf(x)=9 xf(x)=9x, f(x)=4xf(x)=\frac{4}{x}f(x)=x4​.

Problem 3406

Identify the linear function among these equations: f(x)=5−3xf(x)=5-\frac{3}{x}f(x)=5−x3​, f(x)=3x−25f(x)=3x-\frac{2}{5}f(x)=3x−52​, f(x)=4x−52xf(x)=4x-\frac{5}{2x}f(x)=4x−2x5​, f(x)=∣x−4+3∣f(x)=|x-4+3|f(x)=∣x−4+3∣.

Problem 3407

In the expression 3g4\frac{3 g}{4}43g​, what does 3g3 g3g represent in terms of the total gas cost for the trip?

Problem 3408

An ideal gas has a volume of 1.50×10−4 m31.50 \times 10^{-4} \mathrm{~m}^31.50×10−4 m3 at 22∘C22^{\circ} \mathrm{C}22∘C and 1.20×1051.20 \times 10^51.20×105 Pa. Find the temperature in Kelvin when pressure is 2.00×1052.00 \times 10^52.00×105 Pa.

Problem 3409

Complete the table using the function f(x)=x−4f(x)=\sqrt{x-4}f(x)=x−4​. Simplify answers or mark as "Not a real number" if needed.

Problem 3410

Use the function f(x)=x−4f(x)=\sqrt{x-4}f(x)=x−4​ to find f(13)f(13)f(13) and f(85)f(85)f(85). Simplify answers; note non-real results.

Problem 3411

Analyze the function f(x)=∣x−3∣−1f(x)=|x-3|-1f(x)=∣x−3∣−1: find domain, range, intercepts, increasing/decreasing intervals, and end behavior.

Problem 3412

Use the function f(x)=x−4f(x)=\sqrt{x-4}f(x)=x−4​ to complete the table. Simplify answers; mark "Not a real number" if needed.

Problem 3413

Fill in the table using f(x)=x−4f(x)=\sqrt{x-4}f(x)=x−4​. For x=0x=0x=0, 4, 13, and 85, find f(x)f(x)f(x) or state "Not a real number".

Problem 3414

Find values of xxx not in the domain of g(x)=x+5x2−4x−21g(x)=\frac{x+5}{x^{2}-4 x-21}g(x)=x2−4x−21x+5​. List them separated by commas. x=x=x=

Problem 3415

Compare the graphs of g(x)=f(x−2)+7g(x)=f(x-2)+7g(x)=f(x−2)+7 and f(x)f(x)f(x). Which transformation applies?

Problem 3416

Compare the graphs of g(x)=f(x)+5g(x)=f(x)+5g(x)=f(x)+5 and f(x)f(x)f(x): Which shift describes g(x)g(x)g(x) best?

Problem 3417

جد ارتفاع الجسر عند النقطة التي تبعد 6 م عن بدايته، إذا كانت المسافة بين قاعدتيه 24 م وارتفاعه 9 م.

Problem 3418

Problem 3419

Compare the graphs of f(x)=x2f(x)=x^{2}f(x)=x2 and g(x)=4x2g(x)=4x^{2}g(x)=4x2. Which statement is true about their relationship?

Problem 3420

What happens to a function's graph when multiplied by -1? A. Flips over y=xy=xy=x. B. Flips over yyy-axis. C. Flips over xxx-axis.

Problem 3421

Compare g(x)=(13x)2g(x)=\left(\frac{1}{3} x\right)^{2}g(x)=(31​x)2 with f(x)=x2f(x)=x^{2}f(x)=x2. Which transformation describes g(x)g(x)g(x)?

Problem 3422

Compare the graphs of f(x)=x2f(x)=x^{2}f(x)=x2 and g(x)=4x2g(x)=4x^{2}g(x)=4x2. Which statement is true about their relationship?

Problem 3423

What is the new equation when the quadratic function f(x)=x2f(x)=x^{2}f(x)=x2 is shifted right by 12 units? A. g(x)=x2+12g(x)=x^{2}+12g(x)=x2+12 B. g(x)=(x+12)2g(x)=(x+12)^{2}g(x)=(x+12)2 C. g(x)=x2−12g(x)=x^{2}-12g(x)=x2−12 D. g(x)=(x−12)2g(x)=(x-12)^{2}g(x)=(x−12)2

Problem 3424

Find the new function after shifting f(x)=x2f(x)=x^{2}f(x)=x2 right 1 unit, stretching by 5, and reflecting over the xxx-axis.

Problem 3425

What is the equation of the function when the graph of f(x)=x2f(x)=x^{2}f(x)=x2 is flipped over the xxx-axis? A. g(x)=−x2g(x)=-x^{2}g(x)=−x2 B. g(x)=1x2g(x)=\frac{1}{x^{2}}g(x)=x21​ C. g(x)=x−2g(x)=x^{-2}g(x)=x−2 D. g(x)=(−x)2g(x)=(-x)^{2}g(x)=(−x)2

Problem 3426

What is the new equation for the function after stretching f(x)=2xf(x)=2^{x}f(x)=2x vertically by a factor of 3? A. g(x)=2⋅3xg(x)=2 \cdot 3^{x}g(x)=2⋅3x B. g(x)=3⋅2xg(x)=3 \cdot 2^{x}g(x)=3⋅2x C. g(x)=23xg(x)=2^{3 x}g(x)=23x D. g(x)=13⋅2xg(x)=\frac{1}{3} \cdot 2^{x}g(x)=31​⋅2x

Problem 3427

Find the new function from f(x)=xf(x)=xf(x)=x after a vertical stretch by 3 and a flip over the xxx-axis. A. g(x)=3x−1g(x)=3 x-1g(x)=3x−1 B. g(x)=3xg(x)=\frac{3}{x}g(x)=x3​ C. g(x)=−13xg(x)=-\frac{1}{3} xg(x)=−31​x D. g(x)=−3xg(x)=-3 xg(x)=−3x

Problem 3428

What is the new function equation after shifting f(x)=xf(x)=xf(x)=x up 6 units? A. g(x)=16xg(x)=\frac{1}{6} xg(x)=61​x B. g(x)=6xg(x)=6 xg(x)=6x C. g(x)=x−6g(x)=x-6g(x)=x−6 D. g(x)=x+6g(x)=x+6g(x)=x+6

Problem 3429

How does the graph of f(x)=2xf(x)=2^{x}f(x)=2x change to g(x)=3⋅2x+5g(x)=3 \cdot 2^{x}+5g(x)=3⋅2x+5? Select all that apply: A, B, C, D, E.

Problem 3430

Mrs. Hernandez delivers mail for 41.25 min. After 10 min for 5 houses, how to find remaining houses with 1.251.251.25 min each?

Problem 3431

Find the chirp count ccc when the temperature T=90T=90T=90 using the formula T=30+0.28cT=30+0.28cT=30+0.28c. What does ccc represent?

Problem 3432

Mrs. Lopez types words at a rate of 38. Write the equation relating words www and minutes mmm: w=38mw = 38mw=38m.

Problem 3433

Calculate cos⁡48∘\cos 48^{\circ}cos48∘ and round to two decimal places. Options: A. 0.50 B. 1 C. 0.67 D. 0.48 E. None.

Problem 3434

Choose the graph of the function h(x)=13x2h(x)=\frac{1}{3} x^{2}h(x)=31​x2 and its parent function.

Problem 3435

Find the tangent line equation for f(x)=3−xf(x)=\sqrt{3-x}f(x)=3−x​ at a given point.

Problem 3436

Find the derivative of the function y=x4+12xy=x^{4}+12xy=x4+12x. What is dydx\frac{dy}{dx}dxdy​?

Problem 3437

What is the value of a3−b35\frac{a^{3}-b^{3}}{5}5a3−b3​ for a=2a=2a=2 and b=−3b=-3b=−3? Options: −345-3 \frac{4}{5}−354​, −35-\frac{3}{5}−53​, 3, 7.

Problem 3438

Find the values of aaa, bbb, ccc, and ddd in the magic square where rows, columns, and diagonals sum to the same number.

Problem 3439

Doris hat 42 von 60 Punkten. Hat sie bestanden, wenn sie mindestens 75%75\%75% benötigt?

Problem 3440

Simplify tan⁡100∘+4sin⁡100∘\tan 100^{\circ} + 4 \sin 100^{\circ}tan100∘+4sin100∘.

Problem 3441

Identify the linear function from these equations: $f(x)=\frac{3 x+2}{4}$ , $f(x)=\sqrt{x+2}$ , $f(x)=2 x^{2 x-3}$ , $f(x)=\frac{3 x-3}{x^{2}}$ .

Sketch the graph of $f(x)=\frac{3}{x+1}+2$ . Include all 6 axis intersections and asymptotes.

Identify the equation that represents an absolute value function from these options: $f(x)=-9$ , $f(x)=\frac{1}{3 x}$ , $f(x)=x-3 x^{2}$ , $f(x)=\frac{-1}{4}|x+4|-3$ .

Identify the equation that defines a constant function from these options: $f(x)=-\frac{3}{5}$ , $f(x)=3-x$ , $f(x)=9 x$ , $f(x)=\frac{4}{x}$ .

Identify the linear function among these equations: $f(x)=5-\frac{3}{x}$ , $f(x)=3x-\frac{2}{5}$ , $f(x)=4x-\frac{5}{2x}$ , $f(x)=|x-4+3|$ .

In the expression $\frac{3 g}{4}$ , what does $3 g$ represent in terms of the total gas cost for the trip?

An ideal gas has a volume of $1.50 \times 10^{-4} \mathrm{~m}^3$ at $22^{\circ} \mathrm{C}$ and $1.20 \times 10^5$ Pa. Find the temperature in Kelvin when pressure is $2.00 \times 10^5$ Pa.

Complete the table using the function $f(x)=\sqrt{x-4}$ . Simplify answers or mark as "Not a real number" if needed.

Use the function $f(x)=\sqrt{x-4}$ to find $f(13)$ and $f(85)$ . Simplify answers; note non-real results.

Analyze the function $f(x)=|x-3|-1$ : find domain, range, intercepts, increasing/decreasing intervals, and end behavior.

Use the function $f(x)=\sqrt{x-4}$ to complete the table. Simplify answers; mark "Not a real number" if needed.

Fill in the table using $f(x)=\sqrt{x-4}$ . For $x=0$ , 4, 13, and 85, find $f(x)$ or state "Not a real number".

Find values of $x$ not in the domain of $g(x)=\frac{x+5}{x^{2}-4 x-21}$ . List them separated by commas. $x=$

Compare the graphs of $g(x)=f(x-2)+7$ and $f(x)$ . Which transformation applies?

Compare the graphs of $g(x)=f(x)+5$ and $f(x)$ : Which shift describes $g(x)$ best?

Compare the graphs of $f(x)=x^{2}$ and $g(x)=4x^{2}$ . Which statement is true about their relationship?

What happens to a function's graph when multiplied by -1? A. Flips over $y=x$ . B. Flips over $y$ -axis. C. Flips over $x$ -axis.

Compare $g(x)=\left(\frac{1}{3} x\right)^{2}$ with $f(x)=x^{2}$ . Which transformation describes $g(x)$ ?

Compare the graphs of $f(x)=x^{2}$ and $g(x)=4x^{2}$ . Which statement is true about their relationship?

What is the new equation when the quadratic function $f(x)=x^{2}$ is shifted right by 12 units? A. $g(x)=x^{2}+12$ B. $g(x)=(x+12)^{2}$ C. $g(x)=x^{2}-12$ D. $g(x)=(x-12)^{2}$

Find the new function after shifting $f(x)=x^{2}$ right 1 unit, stretching by 5, and reflecting over the $x$ -axis.

What is the equation of the function when the graph of $f(x)=x^{2}$ is flipped over the $x$ -axis? A. $g(x)=-x^{2}$ B. $g(x)=\frac{1}{x^{2}}$ C. $g(x)=x^{-2}$ D. $g(x)=(-x)^{2}$

What is the new equation for the function after stretching $f(x)=2^{x}$ vertically by a factor of 3? A. $g(x)=2 \cdot 3^{x}$ B. $g(x)=3 \cdot 2^{x}$ C. $g(x)=2^{3 x}$ D. $g(x)=\frac{1}{3} \cdot 2^{x}$

Find the new function from $f(x)=x$ after a vertical stretch by 3 and a flip over the $x$ -axis. A. $g(x)=3 x-1$ B. $g(x)=\frac{3}{x}$ C. $g(x)=-\frac{1}{3} x$ D. $g(x)=-3 x$

What is the new function equation after shifting $f(x)=x$ up 6 units? A. $g(x)=\frac{1}{6} x$ B. $g(x)=6 x$ C. $g(x)=x-6$ D. $g(x)=x+6$

How does the graph of $f(x)=2^{x}$ change to $g(x)=3 \cdot 2^{x}+5$ ? Select all that apply: A, B, C, D, E.

Mrs. Hernandez delivers mail for 41.25 min. After 10 min for 5 houses, how to find remaining houses with $1.25$ min each?

Find the chirp count $c$ when the temperature $T=90$ using the formula $T=30+0.28c$ . What does $c$ represent?

Mrs. Lopez types words at a rate of 38. Write the equation relating words $w$ and minutes $m$ : $w = 38m$ .

Calculate $\cos 48^{\circ}$ and round to two decimal places. Options: A. 0.50 B. 1 C. 0.67 D. 0.48 E. None.

Choose the graph of the function $h(x)=\frac{1}{3} x^{2}$ and its parent function.

Find the tangent line equation for $f(x)=\sqrt{3-x}$ at a given point.

Find the derivative of the function $y=x^{4}+12x$ . What is $\frac{dy}{dx}$ ?

What is the value of $\frac{a^{3}-b^{3}}{5}$ for $a=2$ and $b=-3$ ? Options: $-3 \frac{4}{5}$ , $-\frac{3}{5}$ , 3, 7.

Find the values of $a$ , $b$ , $c$ , and $d$ in the magic square where rows, columns, and diagonals sum to the same number.

Doris hat 42 von 60 Punkten. Hat sie bestanden, wenn sie mindestens $75\%$ benötigt?

Simplify $\tan 100^{\circ} + 4 \sin 100^{\circ}$ .

Deposit $\$ P$ for 2 years at $8\%$ p.a. Find interest for (i) simple interest and (ii) compound interest. If difference is $\$ 240$ , find $P$ .

Find $\lim _{x \rightarrow \infty} \cos \left(\frac{1+\pi x}{x}\right)$ .

Given sides $a=5$ and $b=12$ , find $c$ , $\sin B$ , $\cos B$ , $\tan B$ , and $\sec B$ .

Identify the parent function and transformations for: $y=2|x+4|+4$ .

Find the value of $\csc 45^{\circ}$ . Simplify your answer with integers or fractions.

What does $1+x$ represent in the markup price expression $937(1+x)$ for a computer?

Rewrite $\sin 61^{\circ}$ using its cofunction. What is $\sin 61^{\circ}=$ ? (Provide the answer without the degree symbol.)

Rewrite $\tan 38^{\circ}$ using its cofunction. What is the simplified answer?

Calculate the exact value of $\sec 30^{\circ}$ . Simplify your answer with integers or fractions.

Find the exact value of $\sin 60^{\circ}$ . Simplify your answer with radicals, integers, or fractions.

Find the exact value of $\tan 30^{\circ}$ . Simplify your answer with integers or fractions.

Rewrite $\tan 74^{\circ}$ using its cofunction. What is $\tan 74^{\circ}=$ ? Simplify your answer without the degree symbol.

Calculate the exact value of $\csc 45^{\circ}$ . Simplify your answer using integers or fractions.

What will a union member's salary be in 9 years if it increases by $5\%$ annually from a current salary of \$87,300?

Find the graph of $g(x)=\frac{1}{4} f(x)$ given $f(x)=x^{2}$ .

Find $h(6)$ if $h(x) = x^{2} - 4$ .

Find $f(0)$ for the function $f(x)=2x+3$ .

Find $f(-4)$ for the function $f(x)=5x-12$ .

Find the limit as $x$ approaches 4 for the piecewise function $f(x)$ defined as: $f(x) = -7x + 46$ if $x < 4$ , $12$ if $x = 4$ , $2x^2 - 14$ if $x > 4$ . What is $\lim_{x \rightarrow 4} f(x)$ ?

A ball is thrown with a velocity of $41 \mathrm{ft} / \mathrm{s}$ . Its height is $y=41 t-22 t^{2}$ . Find average velocity from $t=2$ and instantaneous velocity at $t=2$ .

Find the rate of change of the city's population modeled by $P(t)=22 e^{0.08 t}$ from 2025 to 2034.

Graph $f(x)=\frac{|x+2|}{x+2}$ for the range $[-4,4]$ .

Graph $f(x)=\frac{|x+3|}{x+3}$ for $x$ in the range $[-4,4]$ .

Find the average rate of change of infections from day 0 to day 16, given $P(0) = 3$ , $P(8) \approx 5.55$ , $P(16) \approx 10.28$ . Round to two decimal places in thousand people per day.

Find the $y$ -coordinate of the vertex of the parabola $g$ given points (-1, 1), (3, 9), (4, 6) and $x=2$ .

Find the value of $k$ for the quadratic function $y=f(x)$ passing through $(5,1),(7,k),(9,26)$ with average rate change of 1.5.

Find $\theta$ using the equation $\cos \theta=\frac{5}{12}$ . Round to the nearest degree if necessary.

Encuentra la derivada de $f(x) = 3x^3 - x$ .