which function is shown in the graph below?

$y = 2^{x-2} + 3$
$y = 2^{x+2} + 3$
$y = 2^{x-3} + 2$
$y = 2^{x+3} + 2$

Question

which function is shown in the graph below?

$y = 2^{x-2} + 3$
$y = 2^{x+2} + 3$
$y = 2^{x-3} + 2$
$y = 2^{x+3} + 2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponential Transformations", "Asymptotic Behavior" ], "new_concepts": [], "current_concepts": [ "Exponential Transformations", "Asymptotic Behavior", "Exponential Growth" ] } ## Identify the horizontal asymptote from the graph $$ y = 3 $$ ## Determine the vertical shift from the asymptote $$ \begin{aligned} &\text{General form: } y = a \cdot b^{x-h} + k \ &k = 3 \end{aligned} $$ ## Use a key point on the graph to find the horizontal shift $$ \begin{aligned} &\text{Point on graph: } (0, 7) \ &7 = 2^{0-h} + 3 \ &4 = 2^{-h} \ &2^2 = 2^{-h} \ &h = -2 \ &y = 2^{x+2} + 3 \end{aligned} $$

(A) $y = 2^{x-2} + 3$

(B) $y = 2^{x+2} + 3$

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

(D) $y = 2^{x+3} + 2$

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

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QUESTION IMAGE

Question

Explanation:

Identify the horizontal asymptote from the graph

Determine the vertical shift from the asymptote

Use a key point on the graph to find the horizontal shift

Answer: