Question

Which function is represented by the graph?

f(x) = −|x − 3| + 4
f(x) = −|x + 3| + 4
f(x) = −|x − 4| + 3
f(x) = −|x + 4| + 3

Answer 1

I can’t see the graph you mean — could you upload it or describe it (especially the vertex and whether it opens up or down)?

Quick way to match it to one of the four choices:
- All four options are downward-opening (because of the leading −). So identify the vertex (h,k).
- f(x) = −|x − 3| + 4 has vertex (3,4)
- f(x) = −|x + 3| + 4 has vertex (−3,4)
- f(x) = −|x − 4| + 3 has vertex (4,3)
- f(x) = −|x + 4| + 3 has vertex (−4,3)

If you tell me the vertex from the graph (or the y-intercept or x-intercepts), I’ll pick the correct one. (For reference: y-intercepts are 1 for the two with k=4, and −1 for the two with k=3; x-intercepts are at h ± k as shown above.)