which exponential function is represented by the graph?

$f(x) = 2(3^x)$
$f(x) = 3(3^x)$
$f(x) = 3(2^x)$
$f(x) = 2(2^x)$

Question

which exponential function is represented by the graph?

$f(x) = 2(3^x)$
$f(x) = 3(3^x)$
$f(x) = 3(2^x)$
$f(x) = 2(2^x)$

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 Functions", "Y-Intercept" ], "new_concepts": [], "current_concepts": [ "Exponential Functions", "Y-Intercept" ] } ## Identify the y-intercept Using the *Y-Intercept* knowledge point $$ \begin{aligned} &f(0) = 3\ &f(x) = a \cdot b^x \implies a \cdot b^0 = a \implies a = 3 \end{aligned} $$ ## Determine the base of the function Using the *Exponential Functions* knowledge point $$ \begin{aligned} &f(1) = 6\ &3 \cdot b^1 = 6 \implies b = 2\ &f(x) = 3(2^x) \end{aligned} $$

(A) $f(x) = 2(3^x)$

(B) $f(x) = 3(3^x)$

(C) $f(x) = 3(2^x)$

(D) $f(x) = 2(2^x)$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the y-intercept

Determine the base of the function

Answer: