Chapter 9.5, Problem 14E

To determine

To calculate; the error in describing the transformation of $f(x)=\tan x$ represented by $g(x)=2\tan 5x$ .

Explanation of Solution

The function is of the form $g(x)=a\tan bx$ where $a=2$ and $b=5$ . So, the period is $\frac{\pi }{\left|b\right|}=\frac{\pi }{5}.$

The error is that the horizontal and vertical shrink factors are switched. The correct answer is:

A vertical stretch by a factor $2$ and a horizontal shrink by a factor of $\frac{1}{5}$ .