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{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Exponential Evaluation", "Exponential Function Transformations" ], "new_concepts": [], "current_concepts": [ "Exponential Evaluation", "Exponential Function Transformations", "Vertical Dilation", "Horizontal Dilation" ] } ## Evaluate functions at $x = 0$ Using the *Exponential Evaluation* and *Exponential Function Transformations* knowledge points $$ \begin{aligned} a &= 2^0 = 1\ b &= 3 \cdot 2^0 = 3 \cdot 1 = 3\ c &= 2^{3(0)} = 2^0 = 1 \end{aligned} $$ ## Evaluate functions at $x = 1$ Using the *Exponential Evaluation* and *Exponential Function Transformations* knowledge points $$ \begin{aligned} d &= 2^1 = 2\ e &= 3 \cdot 2^1 = 3 \cdot 2 = 6\ f &= 2^{3(1)} = 2^3 = 8 \end{aligned} $$ | Variable | Value | |---|---| | $a$ | 1 | | $b$ | 3 | | $c$ | 1 | | $d$ | 2 | | $e$ | 6 | | $f$ | 8 | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Function Transformations" ] }

Variable	Value
\(b\)	3
\(c\)	1
\(d\)	2
\(e\)	6
\(f\)	8

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Evaluate functions at \(x = 0\)

Evaluate functions at \(x = 1\)

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