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.

if $h$ is instead negative, the curve shifts

Question

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.

if $h$ is instead negative, the curve shifts

Accepted Answer

{ "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", "Exponential Function Graphs" ], "new_concepts": [ "Exponential Function Transformations" ], "current_concepts": [ "Horizontal Translation", "Exponential Function Graphs", "Exponential Function Transformations" ] } ## Analyze the transformation equation Using the *Horizontal Translation* and *Exponential Function Graphs* knowledge points $$ y = 2^{(x-h)} + k $$ ## Determine the effect of a negative parameter Using the *Horizontal Translation* knowledge point $$ \begin{aligned} &\text{For } h < 0 \text{ (negative value):}\ &x - h = x - (-|h|) = x + |h|\ &\text{This shifts the graph to the left.} \end{aligned} $$ If $h$ is instead negative, the curve shifts left. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Function Transformations" ] }

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Question

Explanation:

Analyze the transformation equation

Determine the effect of a negative parameter

Answer: