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.

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.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Logarithmic Functions", "End Behavior" ], "current_concepts": [ "Logarithmic Functions", "End Behavior", "Horizontal Translation" ] } ## Analyze the domain of the function $$ \begin{aligned} &f(x) = \log(x - 2) \ &x - 2 > 0 \implies x > 2 \end{aligned} $$ ## Evaluate behavior as x increases $$ \begin{aligned} &\lim_{x \to \infty} \log(x - 2) = \infty \end{aligned} $$ ## Evaluate behavior as x approaches the vertical asymptote $$ \begin{aligned} &\lim_{x \to 2^+} \log(x - 2) = -\infty \end{aligned} $$

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.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Logarithmic Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the domain of the function

Evaluate behavior as x increases

Evaluate behavior as x approaches the vertical asymptote

Answer: