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

Question

(1 point)
Responses

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.

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

The parent function was vertically translated up.

Answer 1

To determine how the parent function \( f(x) = |x| \) was dilated to result in a new graphed function, we need to analyze the characteristics of the original function and how dilations affect it.

1. Vertical translations (up or down) would shift the entire graph of the function without changing its shape.
2. Horizontal stretches would make the graph wider, and horizontal compressions would make the graph narrower.
3. Vertical stretches or compressions would change the height of the V-shape but also shift the entire graph when combined with translations.

Without the specific graph to analyze, I would need to know if the function has been stretched or compressed, or translated. If the V-shape remained the same but was moved vertically, that would indicate a vertical translation. If the V-shape became wider or narrower, that suggests horizontal stretches or compressions.

Given this information, if you describe how the graph appears compared to \( f(x) = |x| \), I'll be able to help you choose the correct response from your options!