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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 compressed.
The parent function was horizontally compressed.

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

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 transformed to produce the given V-shaped graph, we need to consider the specific changes made to the function.

  1. Horizontal Compression: This occurs if the function is of the form \( f(kx) \) where \( k > 1 \). It makes the graph narrower.

  2. Horizontal Stretch: This occurs if the function is of the form \( f(kx) \) where \( 0 < k < 1 \). It makes the graph wider.

  3. Vertical Translation Up: This is represented by adding a positive constant, resulting in a graph that shifts upwards.

  4. Vertical Translation Down: This is represented by subtracting a constant, resulting in a graph that shifts downwards.

Without the specific details of how the graph differs from the standard \( f(x) = |x| \), if the V-shape appears narrower than the parent graph, then it would indicate a horizontal compression (for example, if the function were something like \( f(2x) \)). If it were wider, it would indicate a horizontal stretch.

Since we don't have the exact graph, I cannot definitively say which statement is correct. However, if you observe that the V-shape is narrower than normal, you would choose "The parent function was horizontally compressed." If it is wider, you would choose "The parent function was horizontally stretched." If it only translates up or down, then those respective options would be chosen.

Please refer back to your graph to identify which transformation has occurred. Would you like me to help interpret more details if you provide them?