Chapter C, Problem 40E

To determine

To graph:

The following function with the help of the transformation:

  $y=\left|\sin x\right|$

Explanation of Solution

Given information:

  $y=\left|\sin x\right|$

Graph:

  

Graph 1: $y=\sin x$

  

Graph 2: $y=\left|\sin x\right|$

Interpretation:

Need to draw a first graph of the function $y=\cos x$ as shown by the graph 1. Except positive output, need to recall all possible values of function or sine to take same domain as original.

For example:

One cycle of sine where $x$ in interval $\left[0-2\pi \right]$ , in this case the function is already positive. For the remainder of cycle $y$ should be negative. So, here graph changes from original.

The same shape is observed for the second half of the graph, except its flipped shape across $x$ axis which results that $y$ values are positive.