Question

Use the table to answer the question.

This table presents four options comparing the domain, range, and behavior (increasing or decreasing) of two functions.
Option #1 Option #2 Option #3 Option #4
The functions have the same domain. The functions have the same domain. The functions have different domains. The functions have different domains.
The functions have the same range. The functions have different ranges. The functions have the same range. The functions have different ranges.
Both functions are decreasing. Both functions are decreasing. Both functions are increasing. Both functions are increasing.
Compare the graphs of f(x)=4x−−√
and g(x)=4x−−√3
. Which of the options describing the graphs is true?

(1 point)
Responses

Option #3
Option #3

Option #2
Option #2

Option #4
Option #4

Option #1

Answer 1

Option #3.

Reason: f(x)=√(4x) has domain x ≥ 0 while g(x)=√(4x−3) has domain x ≥ 3/4, so the domains are different. Both outputs are square roots, so the ranges are [0, ∞) (the same). Each square-root function is increasing on its domain, so both functions are increasing.