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

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

The parent function was vertically translated down.
The parent function was vertically translated down.

The parent function was horizontally stretched.
The parent function was horizontally stretched.
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1 answer

To determine how the parent function \( f(x) = |x| \) was dilated to result in the V-shaped graph described, we need to consider what types of transformations affect the shape and position of the graph.

  1. Vertical Translation: Moving the graph up or down affects the y-values but does not change the shape of the V.

  2. Horizontal Compression: This would affect how steep the V appears, but it does not apply to the described transformation without specific information about how the graph has changed.

  3. Vertical Translation Down: Similar to vertical translation up, this would change the position but not the shape itself.

  4. Horizontal Stretch: This would cause the graph to widen, making it less steep.

Without the specific graph in front of us, we can only analyze the general transformations:

  • If the V is steeper compared to \( f(x) = |x| \), that implies a horizontal compression.
  • If the V is wider than \( f(x) = |x| \), that implies a horizontal stretch.

Since there are no indications of vertical translations in the options, either horizontal compression or horizontal stretch is likely correct.

Based on the options provided, if the graph appears to be steeper (narrower V), then the correct answer is:

The parent function was horizontally compressed.

If, however, the graph appears wider (broader V), then the correct response would be:

The parent function was horizontally stretched.

Please check the graph to confirm the shape before selecting the answer.