# 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 \(f\).

- Will scaling the outputs of \(f\) change the \(x\)-intercepts of the graph? Explain how you know.
- 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 \(f\).

### Problem 5

The table shows some values for an odd function \(f\).

\(x\) | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
---|---|---|---|---|---|---|---|---|---|

\(f(x)\) | -3 | 5 | 0 | 19 | -11 |

Complete the table.

### 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 \(g\).