what is the equation for the logarithmic function shown in the graph?

$ f(x) = \log x + 1 $
$ f(x) = \log(x + 1) $
$ f(x) = \log x - 1 $
$ f(x) = \log(x - 1) $

Question

what is the equation for the logarithmic function shown in the graph?

$ f(x) = \log x + 1 $
$ f(x) = \log(x + 1) $
$ f(x) = \log x - 1 $
$ f(x) = \log(x - 1) $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Logarithmic Function Transformations" ], "new_concepts": [], "current_concepts": [ "Logarithmic Function Transformations", "Logarithmic Functions" ] } ## Identify key features of the parent function Using the *Logarithmic Function Transformations* knowledge point $$ \begin{aligned} &y = \log(x) \text{ has a vertical asymptote at } x = 0\ &\text{The } x\text{-intercept of the parent function is at } (1, 0) \end{aligned} $$ ## Analyze the transformations from the graph Using the *Logarithmic Function Transformations* knowledge point $$ \begin{aligned} &\text{Vertical asymptote is at } x = -1\ &\text{The } x\text{-intercept is shifted to } (0, 0)\ &\text{This indicates a horizontal translation to the left by 1 unit} \end{aligned} $$ ## Determine the equation of the transformed function Using the *Logarithmic Function Transformations* knowledge point $$ \begin{aligned} &f(x) = \log(x - h) + k\ &h = -1 \implies f(x) = \log(x + 1) \end{aligned} $$

(A) $f(x) = \log x + 1$

(B) $f(x) = \log (x + 1)$

(C) $f(x) = \log x - 1$

(D) $f(x) = \log (x - 1)$

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

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QUESTION IMAGE

Question

Explanation:

Identify key features of the parent function

Analyze the transformations from the graph

Determine the equation of the transformed function

Answer: