See the picture below.
Work Step by Step
The parent function is $f(x)=\vert x\vert$ (with red), but the graph of $g(x)=-2\vert x\vert$ (with blue) will be narrower, as the coefficient multplies each y-value of the parent function by $2$ and will also be reflected across the x-axis because of the coefficient of $-1$. For drawing the exact graph of the parent function here is a table of values: $f(-2)=\mid -2\mid=2$ $f(-1)=\mid -1\mid=1$ $f(0)= \mid 0\mid=0$ $f(1)= \mid 1\mid=1$ $f(2)= \mid 2\mid=2$ By the use of graph transformation techniques, the graph is stretched by a factor of $2$ and will also be reflected across the x-axis. For drawing the exact graph of $g(x)$ here is the table of values of the given function: $g(-2)=-2 \mid -2\mid=-4$ $g(-1)=-2 \mid -1\mid=-2$ $g(0)=-2 \mid 0\mid=0$ $g(1)=-2 \mid 1\mid=-2$ $g(2)=-2 \mid 2\mid=-4$