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Absolute Value Function Transformation
An upward parabola of the given function is drawn on the coordinate plane.
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The equation is f left parenthesis x right parenthesis equals 2 times start absolute value x end absolute value. The coordinates of the plotted points are labeled as left parenthesis negative 3 comma 6 right parenthesis, left parenthesis negative 2 comma 4 right parenthesis, left parenthesis negative 1 comma 2 right parenthesis, left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 2 right parenthesis, left parenthesis 2 comma 4 right parenthesis, and left parenthesis 3 comma 6 right parenthesis.

An upward open parabola passes through 5 plotted points on a coordinate plane with x-axis ranging from negative 12 to 12 in increments of 2 and y-axis ranging from negative 6 to 18 in increments of 2.
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The equation is f left parenthesis x right parenthesis equals 4 times x squared. The coordinates of the plotted points are labeled as left parenthesis negative 2 comma 16 right parenthesis, left parenthesis negative 1 comma 4 right parenthesis, vertex at left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 4 right parenthesis, and left parenthesis 2 comma 16 right parenthesis.

Describe the similarities in the transformations of each of the function graphs from their parent function.

(1 point)
Responses

The intercepts of both graphs have changed as a result of the transformation.
The intercepts of both graphs have changed as a result of the transformation.

Both graphs have been vertically compressed.
Both graphs have been vertically compressed.

No changes have been made from the parent function.
No changes have been made from the parent function.

Both graphs have been vertically stretched.
Both graphs have been vertically stretched.

All Answers 1

Answered by GPT-5 mini AI
Both graphs have been vertically stretched.

Reason: f(x)=2|x| and f(x)=4x^2 multiply the parent functions |x| and x^2 by factors greater than 1, causing a vertical stretch (values move away from the x-axis).