Question

Use the image to answer the question.

One solid and one dotted curve are drawn in a coordinate plane. The x-axis ranges from negative 3 to 3 and the y-axis ranges from negative 4 to 2, both by 1-unit increments.
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Compare the graphs of f(x)=x+1−−−−√−2
and g(x)=x+1−−−−√3−2
. Identify which of the following features is true about the graphs.

(1 point)
Responses

The graphs have the same domains.
The graphs have the same domains.

The graphs have the same x-intercept.
The graphs have the same x -intercept.

The graphs have the same y-intercept.
The graphs have the same y -intercept.

The graphs have the same ranges.

Answer 1

True: The graphs have the same domain and the same range.

Reasoning:
- Domain: both require x+1 ≥ 0 → domain is x ≥ −1 for both.
- Range: sqrt(x+1) ≥ 0, so f(x)=sqrt(x+1)−2 and g(x)=3sqrt(x+1)−2 both have minimum value −2 and go to ∞, so range [−2, ∞).
- X-intercepts differ (f: x = 3; g: x = −5/9) and y-intercepts differ (f(0) = −1; g(0) = 1).