Answer
The graph of the given function involves (1) a vertical compression by a factor of $\frac{1}{2}$ and (2) a reflection about the $x$-axis of the parent function $y=|x|$.
Refer to the blue graph below.
Work Step by Step
RECALL:
(1) The graph of $y=-|x|$ involves a reflection about the $x$-axis of the parent function $y=|x|$.
(2) The graph of $y=a|x|$ involves a vertical stretch (when $|a|\gt1$) or a vertical compression (when $0 \lt |a| \lt1$) of the parent function $y=|x|$.
Thus, the function $Y=-\frac{1}{2}|x|$ involves the following transformations of the parent function $y=|x|$:
(1) a vertical compression by a factor of $\frac{1}{2}$; and
(2) a reflection about the $x$-axis.
To graph the given function, perform the following:
(1) vertically compress the graph of $y=|x|$ by a factor of $\frac{1}{2}$.
This can be done by multiplying each $y$-value of $y=|x|$ by $\frac{1}{2}$ (while retaining the value of $x$). Refer to the green graph below.
(2) Reflect the graph in (1) about the $x$-axis.
This can be achieved by changing each $y$-value to its opposite (e.g., from $1$ to $-1$) while retaining the $x$-value.
Refer to the blue graph above.
