which functions represent exponential growth?
$y = f(x)$
$y = h(x)$
$y = g(x)$
$y = k(x)$

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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": false, "concepts_used": [ "Exponential Growth and Decay Behavior" ], "new_concepts": [], "current_concepts": [ "Exponential Growth and Decay Behavior", "Exponential Function Graphs" ] } ## Identify exponential growth behavior Using the *Exponential Growth and Decay Behavior* knowledge point $$ \begin{aligned} &\text{Exponential growth functions of the form } y = ab^x \text{ (with } a > 0, b > 1\text{) increase as } x \to \infty.\ &\text{Graphically, as we move from left to right, the curve rises and } y \to \infty. \end{aligned} $$ ## Analyze each function graph Using the *Exponential Growth and Decay Behavior* knowledge point $$ \begin{aligned} &y = f(x) \text{ (orange curve): decreases as } x \text{ increases } \implies \text{Exponential Decay}\ &y = g(x) \text{ (blue curve): decreases as } x \text{ increases } \implies \text{Exponential Decay}\ &y = h(x) \text{ (green curve): increases as } x \text{ increases } \implies \text{Exponential Growth}\ &y = k(x) \text{ (purple curve): increases as } x \text{ increases } \implies \text{Exponential Growth} \end{aligned} $$ ## Select the correct options Using the *Exponential Growth and Decay Behavior* knowledge point $$ \begin{aligned} &\text{The functions representing exponential growth are } y = h(x) \text{ and } y = k(x). \end{aligned} $$

$y = f(x)$

$y = h(x)$

$y = g(x)$

$y = k(x)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Growth and Decay Behavior" ] }

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Question

Explanation:

Identify exponential growth behavior

Analyze each function graph

Select the correct options

Answer: