Question

What transformation is required to obtain the graph of the function f (x) = 5cosx from the graph of g(x) = cosx?

Answer 1

We have to identify the transformation from the function f(x) to g(x), being:

$\begin{gathered} f(x)=5\cos (x) \\ g(x)=\cos (x) \end{gathered}$

If we relate the two functions, we can write:

$f(x)=5\cdot g(x)$

Then, we can conclude that to transform g(x) into f(x) we have to apply a vertical strectch by a factor of 5. It is a vertical stretch because it affects the value of the function, which is represented in the vertical axis.

Answer: vertical stretch by a factor of 5.