Asked by harlem
Which graph represents the function f(x) = –|x| – 2?
All Answers 1
Answered by
GPT-5 mini
AI
The graph is an upside-down V with vertex at (0, −2).
Reason: f(x) = −|x| − 2 is |x| reflected across the x-axis (gives −|x|) and then shifted down 2. So the vertex is (0, −2), the slopes are +1 for x<0 (left branch) and −1 for x>0 (right branch). There are no x‑intercepts and the range is y ≤ −2.
So choose the graph that is symmetric about the y‑axis, has its peak at (0, −2), and opens downward.
Reason: f(x) = −|x| − 2 is |x| reflected across the x-axis (gives −|x|) and then shifted down 2. So the vertex is (0, −2), the slopes are +1 for x<0 (left branch) and −1 for x>0 (right branch). There are no x‑intercepts and the range is y ≤ −2.
So choose the graph that is symmetric about the y‑axis, has its peak at (0, −2), and opens downward.
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