Question

select the correct answer.

which statement describes the end behavior of this function?
\\(f(x) = \log(x - 2)\\)

• as the value of \\(x\\) decreases, the value of \\(f(x)\\) moves toward positive infinity.
• as the value of \\(x\\) increases, the value of \\(f(x)\\) moves toward positive infinity.
• as the value of \\(x\\) increases, the value of \\(f(x)\\) moves toward negative infinity.
• as the value of \\(x\\) decreases, the value of \\(f(x)\\) moves toward a constant.

Explanation:

Determine the domain of the function

$$ x - 2 > 0 \implies x > 2 $$

Analyze the behavior as x increases

$$ \lim_{x \to \infty} \log(x - 2) = \infty $$

Analyze the behavior as x approaches the boundary

$$ \lim_{x \to 2^+} \log(x - 2) = -\infty $$

Answer:

• As the value of \(x\) decreases, the value of \(f(x)\) moves toward positive infinity.
• As the value of \(x\) increases, the value of \(f(x)\) moves toward positive infinity. (Correct answer)
• As the value of \(x\) increases, the value of \(f(x)\) moves toward negative infinity.
• As the value of \(x\) decreases, the value of \(f(x)\) moves toward a constant.