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

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

f(x) = 4 - 2^x

f(x) = 2^x - 4

Question

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": false, "concepts_used": [ "Exponential Functions", "Function Transformations", "Asymptotes and End Behavior" ], "new_concepts": [], "current_concepts": [ "Exponential Functions", "Function Transformations", "Asymptotes and End Behavior" ] } ## Identify key points and asymptotes from the graph $$ \begin{aligned} &\text{Horizontal Asymptote: } y = 0 \text{ as } x \to -\infty\ &\text{Y-intercept: } (0, -0.25)\ &\text{Key point: } (2, -1) \end{aligned} $$ ## Test the given options with the key points $$ \begin{aligned} &\text{Option 1: } f(x) = -2^{x-2}\ &f(0) = -2^{-2} = -0.25\ &f(2) = -2^{0} = -1\ &\text{Option 2: } f(x) = 2^{2-x}\ &f(2) = 2^{0} = 1 eq -1\ &\text{Option 3: } f(x) = 4 - 2^x\ &f(2) = 4 - 4 = 0 eq -1\ &\text{Option 4: } f(x) = 2^x - 4\ &f(2) = 4 - 4 = 0 eq -1 \end{aligned} $$ ## Verify end behavior of the matching function $$ \begin{aligned} &\lim_{x \to -\infty} -2^{x-2} = 0\ &\lim_{x \to \infty} -2^{x-2} = -\infty \end{aligned} $$

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

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

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

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

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

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QUESTION IMAGE

Question

Explanation:

Identify key points and asymptotes from the graph

Test the given options with the key points

Verify end behavior of the matching function

Answer: