which function is represented by the graph?

$h(x) = \frac{5}{2x}$

$h(x) = 5x^2$

$h(x) = 2(5^x)$

Question

which function is represented by the graph?

$h(x) = \frac{5}{2x}$

$h(x) = 5x^2$

$h(x) = 2(5^x)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponential Function Graphs" ], "new_concepts": [], "current_concepts": [ "Exponential Function Graphs", "Function Comparison" ] } ## Identify key points from the graph $$ \begin{aligned} &(0, 2)\ &(1, 10) \quad \text{(off-screen but consistent with rapid growth for } x < 0\text{)} \end{aligned} $$ ## Test the given options at x = 0 $$ \begin{aligned} &h(0) = \frac{5}{2(0)} \implies \text{undefined}\ &h(0) = 5(0)^2 = 0\ &h(0) = 2(5^0) = 2(1) = 2 \end{aligned} $$ ## Verify behavior of the matching function $$ \begin{aligned} &h(x) = 2(5^x)\ &\lim_{x \to -\infty} 2(5^x) = 0 \quad \text{(matches the horizontal asymptote } y = 0 \text{ as } x \to -\infty\text{)}\ &h(-1) = 2(5^{-1}) = 0.4 \quad \text{(consistent with the graph)} \end{aligned} $$

(A) $h(x) = \frac{5}{2x}$

(B) $h(x) = 5x^2$

(C) $h(x) = 2(5^x)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Function Graphs" ] }

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QUESTION IMAGE

Question

Explanation:

Identify key points from the graph

Test the given options at x = 0

Verify behavior of the matching function

Answer: