Select the correct answer.
What is the range of this radical function?

A.
B.
C.
D.

Ask by Todd Gibbs. in the United States

Mar 31,2025

Question

Select the correct answer. What is the range of this radical function? $$ f(x)=\sqrt{x-2}+4 $$ A. $$ [2, \infty) $$ B. $$ [-2, \infty) $$ C. $$ [4, \infty) $$ D. $$ [-4, \infty) $$

UpStudy AI · Accepted Answer

1. The function is given by $$ f(x) = \sqrt{x-2} + 4 $$.

2. Since the square root is defined only for non-negative arguments, we require:
   $$
   x - 2 \geq 0 \quad \Rightarrow \quad x \geq 2.
   $$

3. The minimum value of the square root, $$ \sqrt{x-2} $$, is $$ 0 $$ when $$ x = 2 $$. Thus,
   $$
   f(2) = \sqrt{2-2} + 4 = 0 + 4 = 4.
   $$

4. As $$ x $$ increases beyond $$ 2 $$, $$ \sqrt{x-2} $$ takes on all non-negative values, causing $$ f(x) $$ to increase without bound.

5. Therefore, the range of $$ f(x) $$ is:
   $$
   [4, \infty).
   $$

6. The correct answer is C. $$ [4, \infty) $$.
The range of the function $$ f(x) = \sqrt{x-2} + 4 $$ is $$ [4, \infty) $$.

Select the correct answer.
What is the range of this radical function?

A.
B.
C.
D.

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