Use the table to answer the question.

Question

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

Answer 1

To analyze the functions \( f(x) = \sqrt{4x} \) and \( g(x) = \sqrt{4x - 3} \), we need to determine their domains, ranges, and behavior (increasing or decreasing).

1. Domains:

   • For \( f(x) = \sqrt{4x} \):

     • The expression under the square root must be non-negative: \[ 4x \geq 0 \implies x \geq 0. \]
     • Thus, the domain of \( f(x) \) is \( [0, \infty) \).

   • For \( g(x) = \sqrt{4x - 3} \):

     • The expression under the square root must be non-negative: [ 4x - 3 \geq 0 \implies 4x \ge