Question

Which function is represented by the graph?

f(x) = −2|x| + 1
f(x) =-1/2 |x| + 1
f(x) = -2|x + 1|
f(x) =-1/2 |x + 1|

Answer 1

I don't see the graph — could you upload it or describe it (vertex coordinates and one or two other points)?

Meanwhile, here's how you can identify the correct function quickly:

1. Locate the vertex (the V's point).
- If the vertex is at (0, 1), the two candidates with that vertex are:
- f(x) = −2|x| + 1 (steeper, opens downward)
- f(x) = −(1/2)|x| + 1 (wider, opens downward)
- If the vertex is at (−1, 0), the two candidates are:
- f(x) = −2|x + 1| (steeper, opens downward)
- f(x) = −(1/2)|x + 1| (wider, opens downward)

2. Determine the steepness (slope of each arm).
- For f(x) = a|x - h| + k with a < 0, the right arm has slope a and the left arm has slope −a.
- If the arms are steep (drop 2 units when x increases by 1), a = −2.
- If the arms are shallow (drop 0.5 units when x increases by 1), a = −1/2.

3. Quick numeric test: pick x = vertex_x + 1 and compute y.
- If vertex at (0,1):
- f(1) = −2(1) + 1 = −1 for −2|x| + 1
- f(1) = −1/2(1) + 1 = 1/2 for −(1/2)|x| + 1
- If vertex at (−1,0):
- f(0) = −2|0 + 1| = −2 for −2|x + 1|
- f(0) = −1/2|0 + 1| = −1/2 for −(1/2)|x + 1|

Tell me the vertex and one other point (or upload the image) and I’ll pick the exact function.