MATH SOLVE

3 months ago

Q:
# 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?

Accepted Solution

A:

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 10πFirst we draw the graph of y=tan(x) Period of tan(x) is πWe 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 10πWhen 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.