Math / Algebra

QuestionEVALUATE Independent Practice
Complete the previous problems, check your solutions, then complete the Lesson Checkpoint below.
Complete the Lesson Reflection above by circling your current understanding of the Learning Goal(s).
1. Find the range of the function $f(x)=-2 x-3$ for the domain $\{-1,0,1\}$
Range: $\qquad$
2. Find the range of the function $f(n)=n^{2}-2 n$ for the domain $\{1,3,5\}$
Range: $\qquad$
Evaluate the function using function notation and interpret the value in context. Natalie wants to know how much money her computer costs each day if she never turns it off. She uses a meter to record the amount of energy her computer uses each day for 30 days.
After recording the cost for 30 days, she determined the cost to run her computer is equal to the function $f(d)$ , where $f(d)=.40 d$ , and $d$ is the number of days.
3. What is the value of $f(d)$ at $f(30)$ ?
4. What is the value of $f(30)$ in context? (1) lifelong Algebra 1A (2024) Module 2

Studdy Solution

STEP 1

What is this asking? We need to find the range of a couple functions given their domain, and then figure out how much Natalie's computer costs to run for 30 days. Watch out! Don't mix up domain and range!
Remember, domain is the input, and range is the output.
Also, make sure to interpret the results in the context of the problem!

STEP 2

1. Find the range of $f(x) = -2x - 3$ .
2. Find the range of $f(n) = n^2 - 2n$ .
3. Calculate $f(30)$ for $f(d) = 0.40d$ .
4. Interpret $f(30)$ .

STEP 3

Alright, let's plug in our first domain value, $x = -1$ , into our function $f(x) = -2x - 3$ .
So, $f(-1) = -2 \cdot (-1) - 3$ .
This simplifies to $f(-1) = 2 - 3 = -1$ .
Our first range value is $-1$ !

STEP 4

Next up, $x = 0$ !
Substituting into our function gives us $f(0) = -2 \cdot (0) - 3 = 0 - 3 = -3$ .
So, our second range value is $-3$ !

STEP 5

Finally, let's plug in $x = 1$ .
We get $f(1) = -2 \cdot (1) - 3 = -2 - 3 = -5$ .
Our third range value is $-5$ !

STEP 6

Putting it all together, the range is $\{-1, -3, -5\}$ .

STEP 7

Let's substitute $n = 1$ into $f(n) = n^2 - 2n$ .
We have $f(1) = (1)^2 - 2 \cdot (1) = 1 - 2 = -1$ .
Our first range value is $-1$ !

STEP 8

Now, let's use $n = 3$ .
We get $f(3) = (3)^2 - 2 \cdot (3) = 9 - 6 = 3$ .
Our second range value is $3$ !

STEP 9

Lastly, we'll plug in $n = 5$ .
This gives us $f(5) = (5)^2 - 2 \cdot (5) = 25 - 10 = 15$ .
Our third range value is $15$ !

STEP 10

So, the range is $\{-1, 3, 15\}$ .

STEP 11

We're given the function $f(d) = 0.40d$ , and we want to find $f(30)$ .
Let's substitute $d = 30$ into the function: $f(30) = 0.40 \cdot (30)$ .

STEP 12

Multiplying gives us $f(30) = 12$ .

STEP 13

Since $f(d)$ represents the cost to run Natalie's computer for $d$ days, $f(30) = 12$ means it costs Natalie $\$12$ to run her computer for 30 days.

STEP 14

For $f(x) = -2x - 3$ , the range is $\{-1, -3, -5\}$ .
For $f(n) = n^2 - 2n$ , the range is $\{-1, 3, 15\}$ . $f(30) = 12$ , meaning it costs Natalie $\$12$ to run her computer for 30 days.

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Studdy Solution

STEP 1

STEP 2

1. Find the range of $f(x) = -2x - 3$ .
2. Find the range of $f(n) = n^2 - 2n$ .
3. Calculate $f(30)$ for $f(d) = 0.40d$ .
4. Interpret $f(30)$ .

STEP 3

Alright, let's plug in our first domain value, $x = -1$ , into our function $f(x) = -2x - 3$ .
So, $f(-1) = -2 \cdot (-1) - 3$ .
This simplifies to $f(-1) = 2 - 3 = -1$ .
Our first range value is $-1$ !

STEP 4

Next up, $x = 0$ !
Substituting into our function gives us $f(0) = -2 \cdot (0) - 3 = 0 - 3 = -3$ .
So, our second range value is $-3$ !

STEP 5

Finally, let's plug in $x = 1$ .
We get $f(1) = -2 \cdot (1) - 3 = -2 - 3 = -5$ .
Our third range value is $-5$ !

STEP 6

Putting it all together, the range is $\{-1, -3, -5\}$ .

STEP 7

Let's substitute $n = 1$ into $f(n) = n^2 - 2n$ .
We have $f(1) = (1)^2 - 2 \cdot (1) = 1 - 2 = -1$ .
Our first range value is $-1$ !

STEP 8

Now, let's use $n = 3$ .
We get $f(3) = (3)^2 - 2 \cdot (3) = 9 - 6 = 3$ .
Our second range value is $3$ !

STEP 9

Lastly, we'll plug in $n = 5$ .
This gives us $f(5) = (5)^2 - 2 \cdot (5) = 25 - 10 = 15$ .
Our third range value is $15$ !

STEP 10

So, the range is $\{-1, 3, 15\}$ .

STEP 11

We're given the function $f(d) = 0.40d$ , and we want to find $f(30)$ .
Let's substitute $d = 30$ into the function: $f(30) = 0.40 \cdot (30)$ .

STEP 12

Multiplying gives us $f(30) = 12$ .

STEP 13

Since $f(d)$ represents the cost to run Natalie's computer for $d$ days, $f(30) = 12$ means it costs Natalie $\$12$ to run her computer for 30 days.

STEP 14

For $f(x) = -2x - 3$ , the range is $\{-1, -3, -5\}$ .
For $f(n) = n^2 - 2n$ , the range is $\{-1, 3, 15\}$ . $f(30) = 12$ , meaning it costs Natalie $\$12$ to run her computer for 30 days.

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Studdy Solution

STEP 1

STEP 2

1. Find the range of f(x)=−2x−3f(x) = -2x - 3f(x)=−2x−3.2. Find the range of f(n)=n2−2nf(n) = n^2 - 2nf(n)=n2−2n.3. Calculate f(30)f(30)f(30) for f(d)=0.40df(d) = 0.40df(d)=0.40d.4. Interpret f(30)f(30)f(30).

STEP 3

STEP 4

Next up, x=0x = 0x=0!Substituting into our function gives us f(0)=−2⋅(0)−3=0−3=−3f(0) = -2 \cdot (0) - 3 = 0 - 3 = -3f(0)=−2⋅(0)−3=0−3=−3.So, our **second range value** is −3-3−3!

STEP 5

Finally, let's plug in x=1x = 1x=1.We get f(1)=−2⋅(1)−3=−2−3=−5f(1) = -2 \cdot (1) - 3 = -2 - 3 = -5f(1)=−2⋅(1)−3=−2−3=−5.Our **third range value** is −5-5−5!

STEP 6

Putting it all together, the **range** is {−1,−3,−5}\{-1, -3, -5\}{−1,−3,−5}.

STEP 7

Let's **substitute** n=1n = 1n=1 into f(n)=n2−2nf(n) = n^2 - 2nf(n)=n2−2n.We have f(1)=(1)2−2⋅(1)=1−2=−1f(1) = (1)^2 - 2 \cdot (1) = 1 - 2 = -1f(1)=(1)2−2⋅(1)=1−2=−1.Our **first range value** is −1-1−1!

STEP 8

Now, let's use n=3n = 3n=3.We get f(3)=(3)2−2⋅(3)=9−6=3f(3) = (3)^2 - 2 \cdot (3) = 9 - 6 = 3f(3)=(3)2−2⋅(3)=9−6=3.Our **second range value** is 333!

STEP 9

Lastly, we'll **plug in** n=5n = 5n=5.This gives us f(5)=(5)2−2⋅(5)=25−10=15f(5) = (5)^2 - 2 \cdot (5) = 25 - 10 = 15f(5)=(5)2−2⋅(5)=25−10=15.Our **third range value** is 151515!

STEP 10

So, the **range** is {−1,3,15}\{-1, 3, 15\}{−1,3,15}.

STEP 11

We're given the function f(d)=0.40df(d) = 0.40df(d)=0.40d, and we want to find f(30)f(30)f(30).Let's **substitute** d=30d = 30d=30 into the function: f(30)=0.40⋅(30)f(30) = 0.40 \cdot (30)f(30)=0.40⋅(30).

STEP 12

Multiplying gives us f(30)=12f(30) = 12f(30)=12.

STEP 13

Since f(d)f(d)f(d) represents the cost to run Natalie's computer for ddd days, f(30)=12f(30) = 12f(30)=12 means it costs Natalie $12\$12$12 to run her computer for **30 days**.

STEP 14

For f(x)=−2x−3f(x) = -2x - 3f(x)=−2x−3, the range is {−1,−3,−5}\{-1, -3, -5\}{−1,−3,−5}.For f(n)=n2−2nf(n) = n^2 - 2nf(n)=n2−2n, the range is {−1,3,15}\{-1, 3, 15\}{−1,3,15}. f(30)=12f(30) = 12f(30)=12, meaning it costs Natalie $12\$12$12 to run her computer for 30 days.

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1. Find the range of $f(x) = -2x - 3$ .
2. Find the range of $f(n) = n^2 - 2n$ .
3. Calculate $f(30)$ for $f(d) = 0.40d$ .
4. Interpret $f(30)$ .

Next up, $x = 0$ !
Substituting into our function gives us $f(0) = -2 \cdot (0) - 3 = 0 - 3 = -3$ .
So, our second range value is $-3$ !

Finally, let's plug in $x = 1$ .
We get $f(1) = -2 \cdot (1) - 3 = -2 - 3 = -5$ .
Our third range value is $-5$ !

Putting it all together, the range is $\{-1, -3, -5\}$ .

Let's substitute $n = 1$ into $f(n) = n^2 - 2n$ .
We have $f(1) = (1)^2 - 2 \cdot (1) = 1 - 2 = -1$ .
Our first range value is $-1$ !

Now, let's use $n = 3$ .
We get $f(3) = (3)^2 - 2 \cdot (3) = 9 - 6 = 3$ .
Our second range value is $3$ !

Lastly, we'll plug in $n = 5$ .
This gives us $f(5) = (5)^2 - 2 \cdot (5) = 25 - 10 = 15$ .
Our third range value is $15$ !

So, the range is $\{-1, 3, 15\}$ .

We're given the function $f(d) = 0.40d$ , and we want to find $f(30)$ .
Let's substitute $d = 30$ into the function: $f(30) = 0.40 \cdot (30)$ .

Multiplying gives us $f(30) = 12$ .

Since $f(d)$ represents the cost to run Natalie's computer for $d$ days, $f(30) = 12$ means it costs Natalie $\$12$ to run her computer for 30 days.

For $f(x) = -2x - 3$ , the range is $\{-1, -3, -5\}$ .
For $f(n) = n^2 - 2n$ , the range is $\{-1, 3, 15\}$ . $f(30) = 12$ , meaning it costs Natalie $\$12$ to run her computer for 30 days.