Question

Question

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.
The parent function was vertically translated down.
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Answer 1

To determine how the parent function \(f(x) = |x|\) was transformed into the graphed function, we need to analyze the characteristics of the graph.

1. Upward Facing V Shape: The parent function \(f(x) = |x|\) is already an upward facing V shape.
2. Dilation: A horizontal stretch or compression would change the width of the V shape, while a vertical translation would move the graph up or down without affecting its shape.

Since the prompt refers to a V-shape on the coordinate plane and the ranges provided are typical for a standard V shape (\(f(x) = |x|\)), we would need to know if there was any change to the width or height.

• Horizontal Stretch/Compression: If the graph appeared wider (a horizontal stretch), the function might be of the form \(f(x) = |kx|\) where \(k < 1\). If the graph is narrower (a horizontal compression), then \(k > 1\).
• Vertical Translation: This would be indicated if the vertex of the V shape were shifted up or down compared to the standard \(y = 0\) of \(f(x) = |x|\).

Without the visual reference of the graph, if we have a standard V shape with the vertex at the origin, it suggests there may not have been a vertical translation (up or down).

Based on the information provided and standard transformations of absolute value functions, if the graph appears the same but simply shifted up or down, the appropriate response would typically be vertical translation, either up or down depending on visual evidence.

Conclusion:

If the graph of the transformed function appears to have the same shape and vertex as the parent function, it likely involves one of the stated transformations.

However, if you are claiming that the function was "dilated," it generally means a horizontal stretch or compression, which alters width without vertical translation.

So, based on standard conventions without seeing the image, a proper response could hinge on whether the vertical position had changed.

If additional concrete graphical characteristics were provided in the question, they should be used to finalize the answer. In summary, without knowing the specific changes, the answer would typically be one of the options related to vertical transformation unless specific stretching/compression proportions were defined based on width appearance.

Given the pairs of potential answers, the best inference would be to choose the correct response accordingly based on the graph's characteristics regarding vertical translations or dilations explicitly stated.