question 16
2 pts
describe the transformation that produces this graph of the parent function (f(x) = 2^x).

source:
image created for vva via desmos; 2025

reflection; right 1
left 1
right 1
reflection; left 1

Question

question 16
2 pts
describe the transformation that produces this graph of the parent function (f(x) = 2^x).

source:
image created for vva via desmos; 2025

reflection; right 1
left 1
right 1
reflection; left 1

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": [ "Exponential Transformations" ], "new_concepts": [], "current_concepts": [ "Exponential Transformations", "Function Transformations" ] } ## Analyze the parent function behavior Using the *Exponential Transformations* knowledge point $$ \begin{aligned} &f(x) = 2^x\ &f(0) = 1\ &f(1) = 2\ &f(-1) = 0.5 \end{aligned} $$ ## Identify key points on the transformed graph Using the *Exponential Transformations* knowledge point $$ \begin{aligned} &\text{Asymptote: } y = 0\ &\text{Point 1: } (1, -1)\ &\text{Point 2: } (2, -2)\ &\text{Point 3: } (0, -0.5) \end{aligned} $$ ## Determine the transformation equations Using the *Exponential Transformations* knowledge point $$ \begin{aligned} &g(x) = -2^{x-1}\ &g(1) = -2^0 = -1\ &g(2) = -2^1 = -2\ &g(0) = -2^{-1} = -0.5 \end{aligned} $$ ## Match transformations to options Using the *Exponential Transformations* knowledge point $$ \begin{aligned} &\text{Reflection across the x-axis: } y = -f(x)\ &\text{Horizontal shift right by 1 unit: } y = f(x-1)\ &\text{Combined: Reflection; Right 1} \end{aligned} $$

(A) Reflection; Right 1

(B) Left 1

(C) Right 1

(D) Reflection; Left 1

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

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QUESTION IMAGE

Question

Explanation:

Analyze the parent function behavior

Identify key points on the transformed graph

Determine the transformation equations

Match transformations to options

Answer: