Question

The graph of the function y=tan(x) was horizontally stretched so that its period became 10 pi. Which is the equation of the transformed function?

Answer 1

Let the equation of the transformed function be $y=\tan{ax}$, then 

$\frac{\pi}{a} =10\pi \\ \\ \Rightarrow a= \frac{\pi}{10\pi} = \frac{1}{10}$

Therefore, the equation of the transformed function is $y=\tan\left( \frac{1}{10} x\right)$

Answer 2

Answer:

$y=\tan(\frac{x}{10})$ is the equation of transformed function.

Step-by-step explanation:

The graph of the function y=tan(x) was horizontally stretched so that its period became 10π

First we draw the graph of y=tan(x)

Period of tan(x) is π

We need to change period of y π to 10π by horizontal stretch.

Therefore, y=tan(ax)

where, a is horizontal stretch.

Period of y=tan(ax) is 10π

When function change y=tan(x) to y=tan(ax)

Period change π to $\frac{\pi}{a}$

$\frac{\pi}{a}=10\pi$

$a=\frac{1}{10}$

New function after horizontally stretched by factor of 10 would be $y=\tan(\frac{x}{10})$

Please see the attachment of graph and horizontal stretch.

Thus, $y=\tan(\frac{x}{10})$ is the equation of transformed function.