Answer:
[tex]y=\tan(\frac{x}{10})[/tex] 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 [tex]\frac{\pi}{a}[/tex]
[tex]\frac{\pi}{a}=10\pi[/tex]
[tex]a=\frac{1}{10}[/tex]
New function after horizontally stretched by factor of 10 would be [tex]y=\tan(\frac{x}{10})[/tex]
Please see the attachment of graph and horizontal stretch.
Thus, [tex]y=\tan(\frac{x}{10})[/tex] is the equation of transformed function.
