match each graph below with the appropriate function.

a)

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

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

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

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

Question

match each graph below with the appropriate function.

a)

$ 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 features from the graph $$ \begin{aligned} &\text{Horizontal Asymptote: } y = 4 \text{ as } x \to -\infty\ &\text{y-intercept: } (0, 3)\ &\text{x-intercept: } (2, 0) \end{aligned} $$ ## Evaluate the given functions at key points $$ \begin{aligned} &\text{For } f(x) = -2^{x-2}:\ &\quad \lim_{x \to -\infty} f(x) = 0 eq 4\ &\text{For } f(x) = 2^{2-x}:\ &\quad \lim_{x \to -\infty} f(x) = \infty eq 4\ &\text{For } f(x) = 4 - 2^x:\ &\quad \lim_{x \to -\infty} f(x) = 4 - 0 = 4\ &\quad f(0) = 4 - 2^0 = 3\ &\quad f(2) = 4 - 2^2 = 0\ &\text{For } f(x) = 2^x - 4:\ &\quad \lim_{x \to -\infty} f(x) = -4 eq 4 \end{aligned} $$ ## Select the matching function $$ f(x) = 4 - 2^x $$

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

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

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

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

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

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QUESTION IMAGE

Question

Explanation:

Identify key features from the graph

Evaluate the given functions at key points

Select the matching function

Answer: