Question

select the correct answer.

what is the end behavior of this radical function?

\\f(x) = 4\sqrt{x - 6}\\

• as \\(x\\) approaches positive infinity, \\(f(x)\\) approaches positive infinity.
• as \\(x\\) approaches negative infinity, \\(f(x)\\) approaches positive infinity.
• as \\(x\\) approaches positive infinity, \\(f(x)\\) approaches negative infinity.
• as \\(x\\) approaches negative infinity, \\(f(x)\\) approaches negative infinity.

Explanation:

Determine the domain of the radical function

$$
LATEXBLOCK0
$$

Analyze the behavior as x approaches positive infinity

$$
LATEXBLOCK1
$$

Match with the given options

$$ \text{As } x \text{ approaches positive infinity, } f(x) \text{ approaches positive infinity.} $$

Answer:

• (A) As x approaches positive infinity, f(x) approaches positive infinity. (Correct answer)
• (B) As x approaches negative infinity, f(x) approaches positive infinity.
• (C) As x approaches positive infinity, f(x) approaches negative infinity.
• (D) As x approaches negative infinity, f(x) approaches negative infinity.