select the correct answer.

which equation belongs to the same function family as the graphed function?

$g(x) = \sqrt{6x}$

$g(x) = \frac{6}{x}$

$g(x) = 6^x$

$g(x) = 6 \log x$

Question

select the correct answer.

which equation belongs to the same function family as the graphed function?

$g(x) = \sqrt{6x}$

$g(x) = \frac{6}{x}$

$g(x) = 6^x$

$g(x) = 6 \log x$

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", "Function Families" ], "new_concepts": [], "current_concepts": [ "Logarithmic Functions", "Asymptotes", "Function Families" ] } ## Identify the key features of the graphed function $$ \begin{aligned} &\text{Vertical asymptote: } x = 1\ &\text{Domain: } (1, \infty)\ &\text{Range: } (-\infty, \infty)\ &\text{Shape: } \text{Slowly increasing curve characteristic of a logarithmic function} \end{aligned} $$ ## Match the function family to the options $$ \begin{aligned} &g(x) = \sqrt{6x} \quad \Rightarrow \quad \text{Square Root Function}\ &g(x) = \frac{6}{x} \quad \Rightarrow \quad \text{Rational Function}\ &g(x) = 6^x \quad \Rightarrow \quad \text{Exponential Function}\ &g(x) = 6\log x \quad \Rightarrow \quad \text{Logarithmic Function} \end{aligned} $$ ## Select the correct option $$ \text{The graphed function is a logarithmic function, which matches } g(x) = 6\log x. $$

(A) $g(x) = \sqrt{6x}$

(B) $g(x) = \frac{6}{x}$

(C) $g(x) = 6^x$

(D) $g(x) = 6\log x$

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

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QUESTION IMAGE

Question

Explanation:

Identify the key features of the graphed function

Match the function family to the options

Select the correct option

Answer: