what is the range of the function $y = e^x + 1$ graphed below? $y 0$ $y

Question

what is the range of the function $y = e^x + 1$ graphed below? $y > 0$ $y < 0$ $y < 1$ $y > 1$

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": [ "Domain and Range", "Exponential Function Graphs" ], "new_concepts": [], "current_concepts": [ "Domain and Range", "Exponential Function Graphs" ] } ## Analyze the horizontal asymptote Using the **Exponential Function Graphs** knowledge point $$ \begin{aligned} &\text{For } y = e^x + 1,\ &\lim_{x \to -\infty} e^x = 0 \implies \lim_{x \to -\infty} (e^x + 1) = 1\ &\text{Horizontal asymptote is } y = 1 \end{aligned} $$ ## Determine the range of the function Using the **Domain and Range** knowledge point $$ \begin{aligned} &e^x > 0 \quad \forall x \in \mathbb{R}\ &e^x + 1 > 1\ &y > 1 \end{aligned} $$

$y > 0$

$y < 0$

$y < 1$

$y > 1$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Domain and Range" ] }

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Question

Explanation:

Analyze the horizontal asymptote

Determine the range of the function

Answer: