Question

Which function is represented by the graph?

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

Answer 1

I don’t see the graph — could you upload it or describe it? To identify which choice matches, use this checklist:

1. Locate the vertex (h, k).
- If the vertex is at (0, 1) the options with h = 0 are f(x) = −2|x| + 1 or f(x) = |x| + 1.
- If the vertex is at (−1, 0) the options with h = −1 are f(x) = −2|x + 1| or f(x) = |x + 1|.

2. Determine the opening (up or down).
- If it opens up (V shape pointing upward) the coefficient a is positive (|x| form).
- If it opens down (∧ shape) a is negative (−2|...|).

3. Determine the steepness (the value of |a|).
- If moving 1 unit right from the vertex changes y by 1, |a| = 1 (functions without the 2).
- If moving 1 unit right changes y by 2, |a| = 2 (functions with the 2).

Example matches:
- vertex (0,1), opens down with slope 2 → f(x) = −2|x| + 1
- vertex (0,1), opens up with slope 1 → f(x) = |x| + 1
- vertex (−1,0), opens down with slope 2 → f(x) = −2|x + 1|
- vertex (−1,0), opens up with slope 1 → f(x) = |x + 1|

Give the vertex and whether it opens up/down (or upload the graph) and I’ll pick the correct option.