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)

The graphs have the same domains.

The graphs have the same y-intercept.

The graphs have the same ranges.

The graphs have the same x-intercept.
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Answer 1

Answer: The graphs have the same y-intercept.

Reasoning:
- f(x) = √(x+1) − 2 has domain x ≥ −1; g(x) = ∛(x+1) − 2 has domain all real numbers → domains differ.
- f(0) = 1 − 2 = −1 and g(0) = 1 − 2 = −1 → same y‑intercept (0, −1).
- Range of f is [−2, ∞), range of g is (−∞, ∞) → ranges differ.
- x‑intercepts: f: √(x+1) − 2 = 0 ⇒ x = 3; g: ∛(x+1) − 2 = 0 ⇒ x = 7 → different.