which are features of function (g) if (g(x) = 4log(x) + 4)?

(y)-intercept of ((0, 4))
range of ((-infty, infty))
domain of ((4, infty))
(x)-intercept of ((0.1, 0))
vertical asymptote of (x = 0)

Question

which are features of function (g) if (g(x) = 4log(x) + 4)?

(y)-intercept of ((0, 4))
range of ((-infty, infty))
domain of ((4, infty))
(x)-intercept of ((0.1, 0))
vertical asymptote of (x = 0)

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", "Logarithmic Graphs", "Vertical Asymptotes" ], "new_concepts": [ "Logarithmic Function Features" ], "current_concepts": [ "Logarithmic Functions", "Logarithmic Graphs", "Vertical Asymptotes", "Logarithmic Function Features" ] } ## Analyze the domain and vertical asymptote $$ \begin{aligned} &\text{For } g(x) = 4\log(x) + 4:\ &\text{Domain: } x > 0 \implies (0, \infty)\ &\text{Vertical Asymptote: } x = 0\ &\text{y-intercept: None (since } x = 0 \text{ is not in the domain)} \end{aligned} $$ ## Analyze the range $$ \begin{aligned} &\text{Range of any logarithmic function of the form } a\log(x) + b:\ &\text{Range: } (-\infty, \infty) \end{aligned} $$ ## Analyze the x-intercept $$ \begin{aligned} &g(x) = 0 \implies 4\log(x) + 4 = 0\ &\log(x) = -1\ &x = 10^{-1} = 0.1\ &\text{x-intercept: } (0.1, 0) \end{aligned} $$

y-intercept of (0, 4)

range of (-\infty, \infty)

domain of (4, \infty)

x-intercept of (0.1, 0)

vertical asymptote of x = 0

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

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QUESTION IMAGE

Question

Explanation:

Analyze the domain and vertical asymptote

Analyze the range

Analyze the x-intercept

Answer: