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Solution assignment 09 Absolute value |x|

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Assignment 9

Draw the graph of f(x)=\sin^2(|x|)

Solution

We apply the definition of the absolute value and get:

\sin^2(|x|)=\sin^2(x) if x\geq0

\sin^2(|x|)=\sin^2(-x)=[\sin(-x)]^2=[-\sin(x)]^2=\sin^2(x) if x<0

(sin(abs(x)))^2

We may conclude that f(x)=\sin^2(|x|)=\sin^2(x) for all values of  x. See the graph.

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