Math / Algebra

QuestionWhat kind of transformation converts the graph of $f(x)=-2|x|+5$ into the graph of $g(x)=$ $-4|x|+10 ?$ vertical shrink horizontal stretch vertical stretch horizontal shrink

Studdy Solution

STEP 1

What is this asking? How do we change the graph of $-2|x| + 5$ to get the graph of $-4|x| + 10$ ? Watch out! Don't mix up horizontal and vertical stretches and shrinks!
Also, remember that changes inside the absolute value affect horizontal changes, and changes outside affect vertical changes.

STEP 2

1. Rewrite $g(x)$
2. Compare the functions

STEP 3

Let's rewrite $g(x)$ by factoring out a $\textbf{2}$ : $g(x) = -4|x| + 10 = 2(-2|x| + 5).$ Why did we do this?
Because now the stuff inside the parentheses looks just like $f(x)$ !
This is a great first step to comparing the two functions.

STEP 4

Now we can rewrite $g(x)$ in terms of $f(x)$ : Since $f(x) = -2|x| + 5$ , we can see that $g(x) = 2(-2|x| + 5) = 2f(x).$ Boom! Now we have a super clear relationship between $f(x)$ and $g(x)$ .

STEP 5

We found that $g(x) = 2f(x)$ .
This means that the output of $g$ is always twice the output of $f$ for any given input $x$ .
What does this mean for the graph?
It means we're stretching $f(x)$ vertically by a factor of $\textbf{2}$ to get $g(x)$ .
Imagine grabbing the graph of $f(x)$ and pulling it upwards away from the x-axis, making it twice as tall!

STEP 6

Since we're pulling the graph vertically away from the x-axis to make it taller, we have a vertical stretch.

STEP 7

The transformation that converts the graph of $f(x)$ into the graph of $g(x)$ is a vertical stretch.

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QuestionWhat kind of transformation converts the graph of $f(x)=-2|x|+5$ into the graph of $g(x)=$ $-4|x|+10 ?$ vertical shrink horizontal stretch vertical stretch horizontal shrink

Studdy Solution

STEP 1

What is this asking? How do we change the graph of $-2|x| + 5$ to get the graph of $-4|x| + 10$ ? Watch out! Don't mix up horizontal and vertical stretches and shrinks!
Also, remember that changes inside the absolute value affect horizontal changes, and changes outside affect vertical changes.

STEP 2

1. Rewrite $g(x)$
2. Compare the functions

STEP 3

Let's rewrite $g(x)$ by factoring out a $\textbf{2}$ : $g(x) = -4|x| + 10 = 2(-2|x| + 5).$ Why did we do this?
Because now the stuff inside the parentheses looks just like $f(x)$ !
This is a great first step to comparing the two functions.

STEP 4

Now we can rewrite $g(x)$ in terms of $f(x)$ : Since $f(x) = -2|x| + 5$ , we can see that $g(x) = 2(-2|x| + 5) = 2f(x).$ Boom! Now we have a super clear relationship between $f(x)$ and $g(x)$ .

STEP 5

STEP 6

Since we're pulling the graph vertically away from the x-axis to make it taller, we have a vertical stretch.

STEP 7

The transformation that converts the graph of $f(x)$ into the graph of $g(x)$ is a vertical stretch.

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QuestionWhat kind of transformation converts the graph of f(x)=−2∣x∣+5f(x)=-2|x|+5f(x)=−2∣x∣+5 into the graph of g(x)=g(x)=g(x)= −4∣x∣+10?-4|x|+10 ?−4∣x∣+10? vertical shrink horizontal stretch vertical stretch horizontal shrink

Studdy Solution

STEP 1

STEP 2

1. Rewrite g(x)g(x)g(x)2. Compare the functions

STEP 3

STEP 4

STEP 5

STEP 6

Since we're pulling the graph *vertically* away from the x-axis to make it taller, we have a *vertical stretch*.

STEP 7

The transformation that converts the graph of f(x)f(x)f(x) into the graph of g(x)g(x)g(x) is a **vertical stretch**.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionWhat kind of transformation converts the graph of $f(x)=-2|x|+5$ into the graph of $g(x)=$ $-4|x|+10 ?$ vertical shrink horizontal stretch vertical stretch horizontal shrink

1. Rewrite $g(x)$
2. Compare the functions

Since we're pulling the graph vertically away from the x-axis to make it taller, we have a vertical stretch.

The transformation that converts the graph of $f(x)$ into the graph of $g(x)$ is a vertical stretch.