what is the range of the function $y = e^{4x}$? $y 0$ $y 4$

Question

what is the range of the function $y = e^{4x}$? $y < 0$ $y > 0$ $y < 4$ $y > 4$

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 Function Properties" ] } ## Analyze the exponential base and exponent Using the *Range of Exponential Functions* knowledge point $$ \begin{aligned} &y = e^{4x} \ &\text{Base } e \approx 2.718 > 0 \ &4x \in \mathbb{R} \quad \text{for all } x \in \mathbb{R} \end{aligned} $$ ## Determine the range of the function Using the *Range of Exponential Functions* knowledge point $$ \begin{aligned} &e^u > 0 \quad \text{for all } u \in \mathbb{R} \ &\text{Therefore, } y = e^{4x} > 0 \ &\text{Range: } y > 0 \end{aligned} $$

$y < 0$

$y > 0$

$y < 4$

$y > 4$

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

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Question

Explanation:

Analyze the exponential base and exponent

Determine the range of the function

Answer: