exploring dilations of square root functions

dilation - stretching or compressing the graph of a function

move the slider on the graph to graph each function and describe the transformation.

$y = 2\sqrt{x}$
- vertical stretch
- vertical compression
complete

$y = 0.5\sqrt{x}$
- vertical stretch
- vertical compression
done

Question

exploring dilations of square root functions

dilation - stretching or compressing the graph of a function

move the slider on the graph to graph each function and describe the transformation.

$y = 2\sqrt{x}$
- vertical stretch
- vertical compression
complete

$y = 0.5\sqrt{x}$
- vertical stretch
- vertical compression
done

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Vertical Dilation" ], "new_concepts": [], "current_concepts": [ "Vertical Dilation", "Square Root Function Transformations" ] } ## Identify the given function and transformation type Using the *Vertical Dilation* knowledge point $$ \begin{aligned} &y = a\sqrt{x} \quad \text{where} \quad a = 0.5\ &|a| = 0.5 < 1 \end{aligned} $$ ## Determine the geometric effect of the scale factor Using the *Vertical Dilation* knowledge point $$ \begin{aligned} &\text{Since } 0 < |a| < 1 \text{, the graph is compressed vertically toward the } x\text{-axis.}\ &\text{Therefore, the transformation is a vertical compression.} \end{aligned} $$

vertical stretch

vertical compression

{ "elements": [ { "type": "functiongraph", "params": [ { "js": "Math.sqrt(x)", "latex": "y = \sqrt{x}" }, 0, 10 ], "properties": { "strokeColor": "#583C87", "strokeWidth": 2, "dash": 2, "name": "y = \sqrt{x}", "withLabel": true } }, { "type": "functiongraph", "params": [ { "js": "0.5*Math.sqrt(x)", "latex": "y = 0.5\sqrt{x}" }, 0, 10 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3, "name": "y = 0.5\sqrt{x}", "withLabel": true } } ], "timestamps": [0.5, 1.5] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Vertical Dilation" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given function and transformation type

Determine the geometric effect of the scale factor

Answer: