Graphing functions

Question

I am having problems understanding how to graph the product $fg$ when $f(x) = x$ and $g(x) = |x|$.

Any help would be much appreciated!

Answer 1

It might help to rewrite $g(x) = |x|$ as a piecewise function:

$$g(x) = \left \{ \begin{array}{lr} -x & x < 0 \\ x & x \geq 0 \\ \end{array} \right.$$

Then the product is also a piecewise function.

$$(fg)(x) = \left \{ \begin{array}{lr} -x^2 & x < 0 \\ x^2 & x \geq 0 \\ \end{array} \right.$$