Work Step by Step
RECALL: (i) $y=-f(x)$ yields a reflection about the x-axis of the parent function $f(x)$. (ii) $y=f(x) + k$ involves either a vertical shift of $k$ units upward of the parent function when $k\gt 0$ or $|k|$ units downward when $k \lt0$. The graph involves an inverted V, so its parent function is $y=|x|$. Note that compared to the parent function's graph, whose vertex is at $(0, 0)$ and opens upward, the given graph involves the following transformations: (1) A reflection about the x-axis; This makes the tentative equation of the function: $y=-|x|$. (2) A vertical shift of 2 units upward. This makes the equation of the function $y=-|x| + 2$ Thus, the answer is Option (D).