d)

$ f(x) = -2^{x-2} $

$ f(x) = 2^{2-x} $

$ f(x) = 4 - 2^x $

$ f(x) = 2^x - 4 $

Question

d)

$ f(x) = -2^{x-2} $

$ f(x) = 2^{2-x} $

$ f(x) = 4 - 2^x $

$ f(x) = 2^x - 4 $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Exponential Functions", "Function Transformations" ], "new_concepts": [], "current_concepts": [ "Exponential Functions", "Function Transformations", "Asymptotes and End Behavior" ] } ## Identify key points and asymptote from the graph $$ \begin{aligned} &\text{Horizontal Asymptote: } y = 0\ &\text{Y-intercept: } (0, 4)\ &\text{Point on graph: } (2, 1) \end{aligned} $$ ## Test the given options at $x = 0$ $$ \begin{aligned} &f(0) = -2^{0-2} = -2^{-2} = -\frac{1}{4} eq 4\ &f(0) = 2^{2-0} = 2^2 = 4\ &f(0) = 4 - 2^0 = 4 - 1 = 3 eq 4\ &f(0) = 2^0 - 4 = 1 - 4 = -3 eq 4 \end{aligned} $$ ## Verify the correct option at $x = 2$ $$ f(2) = 2^{2-2} = 2^0 = 1 $$

(A) $f(x) = -2^{x-2}$

(B) $f(x) = 2^{2-x}$

(C) $f(x) = 4 - 2^x$

(D) $f(x) = 2^x - 4$

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QUESTION IMAGE

Question

Explanation:

Identify key points and asymptote from the graph

Test the given options at \(x = 0\)

Verify the correct option at \(x = 2\)

Answer: