select the correct answer.

which function has an asymptote at $x = 5$ and an $x$-intercept of $(6,0)$?

$f(x) = \log(x - 5)$
$f(x) = \log(x + 5)$
$f(x) = \log x - 5$
$f(x) = \log x + 5$

Question

select the correct answer.

which function has an asymptote at $x = 5$ and an $x$-intercept of $(6,0)$?

$f(x) = \log(x - 5)$
$f(x) = \log(x + 5)$
$f(x) = \log x - 5$
$f(x) = \log x + 5$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Logarithmic Functions", "Asymptotes" ], "new_concepts": [], "current_concepts": [ "Logarithmic Functions", "Asymptotes", "Graph Intercepts" ] } ## Analyze the vertical asymptote condition $$ \begin{aligned} &\text{For } f(x) = \log(x - c), \text{ the vertical asymptote occurs where the argument is zero: } x - c = 0 \implies x = c.\ &\text{Given asymptote: } x = 5 \implies c = 5 \implies f(x) = \log(x - 5). \end{aligned} $$ ## Verify the x-intercept condition $$ \begin{aligned} &f(6) = \log(6 - 5) = \log(1) = 0.\ &\text{Thus, the point } (6,0) \text{ is indeed the } x\text{-intercept.} \end{aligned} $$

(A) $f(x) = \log(x - 5)$

(B) $f(x) = \log(x + 5)$

(C) $f(x) = \log x - 5$

(D) $f(x) = \log x + 5$

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

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QUESTION IMAGE

Question

Explanation:

Analyze the vertical asymptote condition

Verify the x-intercept condition

Answer: