explore transformations of the basic exponential function $y = 2^x$, shown right. first, change the slider for $h$ to positive values such as 1, 2, or 3. the curve shifts $h$ units dropdown

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Horizontal Translation" ], "new_concepts": [], "current_concepts": [ "Horizontal Translation", "Exponential Function Graphs" ] } ## Analyze the transformation formula Using the *Horizontal Translation* knowledge point $$ y = 2^{(x-h)} + k $$ ## Determine the effect of positive h Using the *Horizontal Translation* knowledge point $$ \begin{aligned} &\text{For } h > 0 \text{ (e.g., } h = 1, 2, 3\text{):}\ &x \to x - h \implies \text{shift to the right by } h \text{ units} \end{aligned} $$ Explore transformations of the basic exponential function $y = 2^x$, shown right. First, change the slider for $h$ to positive values such as 1, 2, or 3. The curve shifts $h$ units right { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Horizontal Translation" ] }

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Analyze the transformation formula

Determine the effect of positive h

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