Lesson 8

Scaling the Outputs

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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.

Graphs of f of x and g of x on grid.

 

Y equals f of x and g of x.
Functions f of x and g of x on grid.
Functions y equals f of x and g of x on grid.

Solution

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Problem 2

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

Graph of 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.

Solution

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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.

Solution

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Problem 4

The dashed function is the graph of \(f\) and the solid function is the graph of \(g\). Express \(g\) in terms of \(f\).

Graph of function f and g.

Solution

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(From Unit 5, Lesson 4.)

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.

Solution

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(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 \(g\).

2 functions.

Solution

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(From Unit 5, Lesson 7.)