Question

Compare the graphs of and
. Identify which of the following features is
true about the graphs.
(1 point)
f (x) = x + 1 − 2 −−−− √
g (x) = x + 1 − 2 −−−− √
3
The graphs have the same domains.
The graphs have the same y-intercept.
The graphs have the same x-intercept.
The graphs have the same ranges.

Answer 1

Interpreting
f(x) = √(x+1) − 2 and g(x) = ∛(x+1) − 2:

- Domains: f: x ≥ −1 (because of the square root). g: all real x (cube root defined for all real). → Domains are different.
- y-intercepts (x=0): f(0)=√1−2=−1, g(0)=∛1−2=−1. → Same y-intercept (0, −1).
- x-intercepts (y=0): f: √(x+1)=2 ⇒ x=3. g: ∛(x+1)=2 ⇒ x=7. → Different x-intercepts.
- Ranges: f: y ≥ −2. g: all real y. → Ranges are different.

So the only true feature is: The graphs have the same y-intercept.