# Lesson 8

Scaling the Outputs

• Let’s stretch and squash some graphs.

### Problem 1

In each pair of graphs shown here, the values of function $$g$$ are the values of function $$f$$ multiplied by a scale factor. Express $$g$$ in terms of $$f$$ using function notation.

### Problem 2

Here is the graph of $$y = f(x)$$ for a cubic function $$f$$.

1. Will scaling the outputs of $$f$$ change the $$x$$-intercepts of the graph? Explain how you know.
2. Will scaling the outputs of $$f$$ change the $$y$$-intercept of the graph? Explain how you know.

### Problem 3

The function $$f$$ is given by $$f(x) = 2^x$$, while the function $$g$$ is given by $$g(x) = 4 \boldcdot 2^x$$. Kiran says that the graph of $$g$$ is a vertical scaling of the graph of $$f$$. Mai says that the graph of $$g$$ is a horizontal shift of the graph of $$f$$. Do you agree with either of them? Explain your reasoning.

### Problem 4

The dashed function is the graph of $$f$$ and the solid function is the graph of $$g$$. Express $$g$$ in terms of $$f$$.

(From Unit 5, Lesson 4.)

### Problem 5

The table shows some values for an odd function $$f$$.

 $$x$$ $$f(x)$$ -4 -3 -2 -1 0 1 2 3 4 -3 5 0 19 -11

Complete the table.

(From Unit 5, Lesson 5.)

### Problem 6

Here is a graph of $$f(x)=x^3$$ and a graph of $$g$$, which is a transformation of $$f$$. Write an equation for the function $$g$$.

(From Unit 5, Lesson 7.)