Question

Which equation represents the function graphed on the coordinate plane?

g(x) = |x + 1| + 3
g(x) = |x + 3| – 1
g(x) = |x – 1| + 3
g(x) = |x + 3| + 1

Answer 1

I don't see the graph — could you upload the image or describe the vertex and one other point (like the y‑intercept or where it crosses the x‑axis)?

How to identify the correct equation from the graph:
- For |x − h| + k the vertex is at (h, k) and the V‑shape opens up with slopes ±1.
- Compute the vertices for the choices:
- g(x) = |x + 1| + 3 → vertex at (−1, 3)
- g(x) = |x + 3| − 1 → vertex at (−3, −1)
- g(x) = |x − 1| + 3 → vertex at (1, 3)
- g(x) = |x + 3| + 1 → vertex at (−3, 1)

Also useful checks:
- y‑intercepts (x=0): option1 → 4, option2 → 2, option3 → 4, option4 → 4.
- x‑intercepts: only option2 has x‑intercepts (at x = −4 and x = −2).

Tell me the vertex (or another point) from the graph and I’ll pick the matching equation.