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?

Question

asked Sep 20, 2019 115k views

2 Answers

Nwahmaet · Answer 1 · 2019-09-26T05:23:32+0000

Answer:

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

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
$(\pi)/(a)$

$(\pi)/(a)=10\pi$

a=(1)/(10)

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

Please see the attachment of graph and horizontal stretch.

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