Question
Horizontal Stretches & Compressions Quick Check
2 of 52 of 5 Items
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 vertically translated down.
The parent function was vertically translated down.
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.
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Answers
Answered by
GPT-4o mini
To determine how the parent function \( f(x) = |x| \) was transformed to create the V-shaped graph mentioned in your question, we need to analyze the image of the graph. Since we don't have the specific image, we can outline how to look for signs of horizontal stretches or compressions:
- **Horizontal Stretch**: If the V-shape is wider than the parent function, it indicates a horizontal stretch. This would occur if the function were transformed into something of the form \( f(x) = |kx| \) with \( 0 < k < 1 \).
- **Horizontal Compression**: If the V-shape is narrower than the parent function, it suggests a horizontal compression. This usually means the function takes the form \( f(x) = |kx| \) where \( k > 1 \).
- **Vertical Translation**: If the entire graph has moved up or down without changing its shape, this indicates a vertical translation.
Based on your question, if the V-shaped graph looks wider than the original function \( f(x) = |x| \), then the correct answer would be:
**The parent function was horizontally stretched.**
Conversely, if the V-shaped graph appears narrower, the answer would be:
**The parent function was horizontally compressed.**
Without the visual, please use the information above to assess the graph you have. If it’s wider, choose “horizontally stretched,” and if it’s narrower, select “horizontally compressed.”
- **Horizontal Stretch**: If the V-shape is wider than the parent function, it indicates a horizontal stretch. This would occur if the function were transformed into something of the form \( f(x) = |kx| \) with \( 0 < k < 1 \).
- **Horizontal Compression**: If the V-shape is narrower than the parent function, it suggests a horizontal compression. This usually means the function takes the form \( f(x) = |kx| \) where \( k > 1 \).
- **Vertical Translation**: If the entire graph has moved up or down without changing its shape, this indicates a vertical translation.
Based on your question, if the V-shaped graph looks wider than the original function \( f(x) = |x| \), then the correct answer would be:
**The parent function was horizontally stretched.**
Conversely, if the V-shaped graph appears narrower, the answer would be:
**The parent function was horizontally compressed.**
Without the visual, please use the information above to assess the graph you have. If it’s wider, choose “horizontally stretched,” and if it’s narrower, select “horizontally compressed.”