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 and
. Which of the options describing the graphs is
true?
(1 point)
f (x) = 4x
−− √
g (x) = 4x

Answer 1

Option 4.

Reason: f(x) = √(4x) = 2√x has domain x ≥ 0, range [0, ∞), and is increasing on its domain. g(x) = 4x has domain all real numbers, range (−∞, ∞), and is increasing. So the domains are different, the ranges are different, and both functions are increasing.