which function has a range of $y

Question

which function has a range of $y < 3$?

$y = 3(2)^x$
$y = 2(3)^x$
$y = -(2)^x + 3$
$y = (2)^x - 3$

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", "Exponential Function Transformations" ], "new_concepts": [], "current_concepts": [ "Range of Exponential Functions", "Exponential Function Transformations" ] } ## Analyze exponential function ranges Using the *Range of Exponential Functions* knowledge point $$ \begin{aligned} &y = a \cdot b^x + k \quad (b > 0, b e 1) \ &\text{If } a > 0, \text{ then } y > k \ &\text{If } a < 0, \text{ then } y < k \end{aligned} $$ ## Evaluate each option Using the *Exponential Function Transformations* and *Range of Exponential Functions* knowledge points $$ \begin{aligned} &\text{Option 1: } y = 3(2)^x \implies a = 3 > 0, k = 0 \implies y > 0 \ &\text{Option 2: } y = 2(3)^x \implies a = 2 > 0, k = 0 \implies y > 0 \ &\text{Option 3: } y = -(2)^x + 3 \implies a = -1 < 0, k = 3 \implies y < 3 \ &\text{Option 4: } y = (2)^x - 3 \implies a = 1 > 0, k = -3 \implies y > -3 \end{aligned} $$ ## Identify the correct function Using the *Range of Exponential Functions* knowledge point $$ y = -(2)^x + 3 \implies \text{Range: } y < 3 $$

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

(B) $y = 2(3)^x$

(C) $y = -(2)^x + 3$

(D) $y = (2)^x - 3$

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

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Question

Explanation:

Analyze exponential function ranges

Evaluate each option

Identify the correct function

Answer: