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{ "quality": "incomplete", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Horizontal Translation", "Exponential Functions", "Function Transformations" ], "current_concepts": [ "Horizontal Translation", "Exponential Functions", "Function Transformations" ] } ## Identify the transformation from $f(x)$ to $g(x)$ $$ g(x) = f(x - 4) = 2^{x - 4} $$ ## Determine key features of the transformed function $$ \begin{aligned} &\text{Horizontal shift:} \quad 4 \text{ units to the right}\ &\text{Horizontal asymptote:} \quad y = 0\ &\text{y-intercept:} \quad g(0) = 2^{-4} = \frac{1}{16}\ &\text{Domain:} \quad (-\infty, \infty)\ &\text{Range:} \quad (0, \infty) \end{aligned} $$ ## Match with standard transformation descriptions $$ \text{The graph of } g(x) \text{ is shifted } 4 \text{ units to the right of the graph of } f(x). $$

(A) The graph of function g is shifted 4 units to the right of the graph of function f.

(B) The graph of function g is shifted 4 units to the left of the graph of function f.

(C) The graph of function g is shifted 4 units up from the graph of function f.

(D) The graph of function g is shifted 4 units down from the graph of function f.

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

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Explanation:

Identify the transformation from \(f(x)\) to \(g(x)\)

Determine key features of the transformed function

Match with standard transformation descriptions

Answer: