Chapter 6 - 6.5 - Graphs of Other Trigonometric Functions - 6.5 Exercises - Page 476: 68

$f(x)=|x|~cos~x=0$ matches with the graph labeled (c).

Work Step by Step

The product of two even functions, $|x|$ and $cos~x$, is an even function, that is, a function whose graph is symmetric with respect to the y-axis: Also, $f(x)=|x|~cos~x=0$, in the interval $[-\frac{3\pi}{2},\frac{3\pi}{2}]$, when $x=-\frac{3\pi}{2},x=-\frac{\pi}{2},x=0,x=\frac{\pi}{2},x=\frac{3\pi}{2}$. These points are the x-intercepts.

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