which steps will translate (f(x) = 3^x) to (g(x) = 3^{x + 1} + 4)?

shift (f(x) = 3^x) one unit up and four units to the right.
shift (f(x) = 3^x) one unit up and four units to the left.
shift (f(x) = 3^x) one unit to the right and four units up.
shift (f(x) = 3^x) one unit to the left and four units up.

Question

which steps will translate (f(x) = 3^x) to (g(x) = 3^{x + 1} + 4)?

shift (f(x) = 3^x) one unit up and four units to the right.
shift (f(x) = 3^x) one unit up and four units to the left.
shift (f(x) = 3^x) one unit to the right and four units up.
shift (f(x) = 3^x) one unit to the left and four units up.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Function Transformations" ], "new_concepts": [], "current_concepts": [ "Exponential Functions", "Function Transformations" ] } ## Identify the transformation components Using the *Function Transformations* knowledge point $$ \begin{aligned} &g(x) = f(x + h) + k \ &g(x) = 3^{x + 1} + 4 \ &h = 1, \quad k = 4 \end{aligned} $$ ## Determine the horizontal shift Using the *Function Transformations* knowledge point $$ \begin{aligned} &f(x + 1) \implies \text{Shift left by } 1 \text{ unit} \end{aligned} $$ ## Determine the vertical shift Using the *Function Transformations* knowledge point $$ \begin{aligned} &+ 4 \implies \text{Shift up by } 4 \text{ units} \end{aligned} $$

Shift $f(x) = 3^x$ one unit up and four units to the right.

Shift $f(x) = 3^x$ one unit up and four units to the left.

Shift $f(x) = 3^x$ one unit to the right and four units up.

Shift $f(x) = 3^x$ one unit to the left and four units up.

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

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QUESTION IMAGE

Question

Explanation:

Identify the transformation components

Determine the horizontal shift

Determine the vertical shift

Answer: