Question

Comparing shapes of Functions Quick Check
Compare the graphs and determine which one could be the graph of a square root function.

Answer 1

I don’t see the graphs you’re comparing. I can’t pick one without the picture, but here are the features to look for so you can tell which graph could be a square‑root function:

Key characteristics of y = a·√(x − h) + k (general square‑root):
- Domain is [h, ∞) — the graph has a left endpoint at x = h and exists only to the right of that point.
- It starts at the endpoint (h, k) and then continues to the right.
- It is monotonic (either increasing if a > 0 or decreasing if a < 0).
- The slope is steep near the endpoint and flattens out as x increases (concave down when a > 0).
- No vertical or horizontal asymptotes, and it is not symmetric about a vertical axis.

Common graphs that are NOT square‑root functions:
- A parabola (symmetric, domain all real numbers).
- An exponential (has a horizontal asymptote, no finite left endpoint).
- A cube‑root (defined for all real x and has an S‑type odd symmetry).
- A line or V (linear or absolute‑value shapes are straight segments).

So pick the graph that has a single left endpoint and then curves to the right, rising quickly at first and then leveling off. If you upload the images or describe each graph briefly, I’ll point out which one is the square‑root.