Question

Begin by graphing the standard absolute value function f(x)=|x|. Then use transformations of this graph to graph the given function.

Answer 1

We have the following:

$h(x)=2|x|-2$

replacing value of x:

$\begin{gathered} h(-2)=2|-2|-2=2\cdot2-2=2\rightarrow(-2,2) \\ h(-1)=2|-1|-2=2\cdot1-2=0\rightarrow(-1,0) \\ h(0)=2|0|-2=0-2=-2\rightarrow(0,-2) \\ h(1)=2|1|-2=2\cdot1-2=0\rightarrow(1,0) \\ h(2)=2|2|-2=2\cdot2-2=2\rightarrow(2,2) \end{gathered}$

The graph is: