Lesson 8
Scaling the Outputs
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.
Solution
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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.
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 \(f\).
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 \(g\).
Solution
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(From Unit 5, Lesson 7.)