select the correct answer.

the graph of $f(x) = \frac{1}{x}$ has been transformed to create the graph of $g(x) = \frac{1}{x} + k$.

what is the value of $k$?

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Question

select the correct answer.

the graph of $f(x) = \frac{1}{x}$ has been transformed to create the graph of $g(x) = \frac{1}{x} + k$.

what is the value of $k$?

0
3
2

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Function Transformations", "Rational Functions", "Asymptotes" ], "new_concepts": [], "current_concepts": [ "Function Transformations", "Rational Functions", "Asymptotes" ] } ## Identify the horizontal asymptote of the parent function $$ \lim_{x \to \pm\infty} f(x) = \lim_{x \to \pm\infty} \frac{1}{x} = 0 $$ ## Determine the horizontal asymptote of the transformed function from the graph $$ y = 3 $$ ## Solve for the vertical shift parameter $$ \begin{aligned} g(x) &= f(x) + k = \frac{1}{x} + k \ \lim_{x \to \pm\infty} g(x) &= k \ k &= 3 \end{aligned} $$

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

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QUESTION IMAGE

Question

Explanation:

Identify the horizontal asymptote of the parent function

Determine the horizontal asymptote of the transformed function from the graph

Solve for the vertical shift parameter

Answer: