which of the following is the graph of this rational function?
\y = \frac{1}{x} + 1\

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Graphing Rational Functions", "Asymptotes of Rational Functions" ], "new_concepts": [], "current_concepts": [ "Graphing Rational Functions", "Asymptotes of Rational Functions" ] } ## Identify the asymptotes of the function Using the *Asymptotes of Rational Functions* knowledge point $$ \begin{aligned} &\text{Vertical asymptote: } x = 0\ &\text{Horizontal asymptote: } y = 1 \end{aligned} $$ ## Evaluate key points on the graph Using the *Graphing Rational Functions* knowledge point $$ \begin{aligned} &x = 1 \implies y = \frac{1}{1} + 1 = 2\ &x = -1 \implies y = \frac{1}{-1} + 1 = 0 \end{aligned} $$ ## Match with the given options Using the *Graphing Rational Functions* knowledge point $$ \begin{aligned} &\text{First graph: passes through } (1, 2) \text{ and } (-1, 0)\text{, with horizontal asymptote } y = 1.\ &\text{Second graph: has horizontal asymptote } y = 0.\ &\text{Third graph: has horizontal asymptote } y = 0 \text{ and passes through } (1, 0). \end{aligned} $$

(A) First graph (left): passes through (1, 2) and (-1, 0) with horizontal asymptote y = 1

(B) Second graph (middle): has horizontal asymptote y = 0

(C) Third graph (right): passes through (1, 0) with horizontal asymptote y = 0

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Question

Explanation:

Identify the asymptotes of the function

Evaluate key points on the graph

Match with the given options

Answer: