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Use the image to answer the question.

A upward facing V-shaped graph is plotted on a coordinate plane. The x-axis ranges from negative 3 to 3 in 1-unit increments and the y-axis ranges from 0 to 3 in 1-unit increments.

Which of the following statements correctly describes how the parent function f(x)=|x|
was dilated to result in the graphed function?

(1 point)
Responses

The parent function was horizontally stretched.
The parent function was horizontally stretched.

The parent function was horizontally compressed.
The parent function was horizontally compressed.

The parent function was vertically translated up.
The parent function was vertically translated up.

The parent function was vertically translated down.

1 answer

To determine how the parent function \( f(x) = |x| \) was dilated to produce the graph described, we need to analyze how the graph has changed.

  1. Horizontal Stretch or Compression: If the graph is wider than the parent function \( f(x) = |x| \), it means that it has been horizontally stretched. If it is narrower, it indicates it has been horizontally compressed.

  2. Vertical Translation: This occurs when the entire graph moves up or down on the y-axis.

From your description, if the graph appears wider than the standard V-shape of \( f(x) = |x| \) (which reaches point (1,1) at x = 1 and (1,1) mirrored on the negative side), then the graph has likely undergone a horizontal stretch.

Therefore, the correct response describing how the parent function has been modified in this context is:

The parent function was horizontally stretched.