Question 16: Given the function \(y = f\left( x \right)\) with the graph of the figure below. How many extremes does the function \(y = f\left( {\left| x \right|} \right)\) have?

Keep the graph to the right of the Oy axis

Symmetric the part of the graph lying on the right of the Oy axis through \(AB’ = 3 \Rightarrow \sqrt {A{B^2} + A{{A’}^2}} = 3\) we get the function graph \ (y = f\left( {\left| x \right|} \right)\).

So the function \(y = f\left( {\left| x \right|} \right)\) has 3 extremes.

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