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?

$y > 0$
$y < 0$
$y < 1$

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": [ "Range of Exponential Functions", "Exponential Function Transformations" ], "new_concepts": [], "current_concepts": [ "Range of Exponential Functions", "Exponential Function Transformations" ] } ## Analyze the parent function range Using the *Range of Exponential Functions* knowledge point $$ e^x > 0 \quad \text{for all } x \in \mathbb{R} $$ ## Apply the vertical translation Using the *Exponential Function Transformations* knowledge point $$ \begin{aligned} y &= e^x + 1 \ y &> 0 + 1 \ y &> 1 \end{aligned} $$ ## Verify with the graph Using the *Range of Exponential Functions* knowledge point $$ \begin{aligned} &\text{Horizontal asymptote: } y = 1 \ &\text{Graph lies entirely above } y = 1 \implies y > 1 \end{aligned} $$

y > 0

y < 0

y < 1

y > 1

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Range of Exponential Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the parent function range

Apply the vertical translation

Verify with the graph

Answer: