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

Question

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

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

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" ], "new_concepts": [], "current_concepts": [ "Range of Exponential Functions", "Exponential Transformations" ] } ## Identify the parent function and its range Using the *Range of Exponential Functions* knowledge point $$ \begin{aligned} &f(x) = e^x \ &\text{Range: } (0, \infty) \quad \text{or} \quad y > 0 \end{aligned} $$ ## Apply the vertical translation Using the *Range of Exponential Functions* knowledge point $$ \begin{aligned} &y = e^x + 1 \ &\text{Range: } (0 + 1, \infty) \quad \text{or} \quad y > 1 \end{aligned} $$ ## 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

Explanation:

Identify the parent function and its range

Apply the vertical translation

Verify with the graph

Answer: