value: 1

which statement is true about the function $y = 0.5|x|$?

a. graph of the function is vertically stretched.
b. graph of the function is horizontally stretched.
c. graph of the function is vertically compressed.
d. graph of the function is horizontally compressed.

Question

value: 1

which statement is true about the function $y = 0.5|x|$?

a. graph of the function is vertically stretched.
b. graph of the function is horizontally stretched.
c. graph of the function is vertically compressed.
d. graph of the function is horizontally compressed.

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": [ "Absolute Value Transformations", "Vertical Compression" ], "new_concepts": [], "current_concepts": [ "Absolute Value Transformations", "Vertical Compression", "Function Transformations" ] } ## Identify the parent function and transformation Using the *Absolute Value Transformations* knowledge point $$ \begin{aligned} &f(x) = |x|\ &g(x) = a \cdot f(x) = 0.5|x|\ &a = 0.5 \end{aligned} $$ ## Analyze the vertical transformation factor Using the *Vertical Compression* knowledge point $$ \begin{aligned} &0 < |a| < 1 \implies 0 < 0.5 < 1\ &\text{The graph is vertically compressed by a factor of } 0.5. \end{aligned} $$

a. Graph of the function is vertically stretched.

b. Graph of the function is horizontally stretched.

c. Graph of the function is vertically compressed.

d. Graph of the function is horizontally compressed.

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QUESTION IMAGE

Question

Explanation:

Identify the parent function and transformation

Analyze the vertical transformation factor

Answer: