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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.
Here is the graph of \(y = f(x)\) for a cubic function \(f\).
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.
The dashed function is the graph of \(f\) and the solid function is the graph of \(g\). Express \(g\) in terms of \(f\).
The table shows some values for an odd function \(f\).
Complete the table.
| \(x\) | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|---|---|---|---|
| \(f(x)\) | -3 | 5 | 0 | 19 | -11 |
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 \(g\).