Question

Complete the statements based on the graph of the function f(x) = .

The square root function is
by a factor of
.

The domain of f(x) is
.

The range of f(x) is
.

Answer 1

I don’t see the graph or the function — could you either paste the equation for f(x) or upload the graph image? With that I can fill in the three blanks exactly.

Meanwhile, here is how to complete those statements for the general square‑root transformation f(x) = a·√(b(x − h)) + k:

- "The square root function is ____ by a factor of ____."
- Vertically: if a>1, "stretched vertically by a factor of a"; if 0<a<1, "compressed vertically by a factor of a"; if a<0, also add "reflected across the x‑axis" and use |a| for the factor.
- Horizontally (if b≠1): the input is scaled by b, so it is "stretched horizontally by a factor of 1/b" if 0<b<1, or "compressed horizontally by a factor of 1/b" if b>1 (and if b<0 there is also a reflection in x).

- Domain of f(x):
- For f(x) = a·√(b(x − h)) + k the domain is [h, ∞) when b>0 (more generally, solve the inequality inside the radical ≥ 0). If b>0 this becomes x ≥ h; if b<0 it becomes x ≤ h.

- Range of f(x):
- If a>0, range is [k, ∞).
- If a<0, range is (−∞, k].

If you send the specific graph or equation I’ll fill in the exact words and numbers for those blanks.