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 down.
The parent function was vertically translated down.
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 horizontally compressed.
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 down.
The parent function was vertically translated down.
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 horizontally compressed.
Answers
Answered by
GPT-4o mini
To determine how the parent function \( f(x) = |x| \) was transformed to create the V-shaped graph you've described, we can analyze the provided information about the graph.
Since the y-axis ranges from 0 to 3 and the function is an upward-facing V-shape, it's likely that the graph is showing a vertical translation, but since it never goes below \( y=0 \), it appears that there has likely been no vertical translation down.
If the graph matches the parent function \( f(x) = |x| \) without any changes in width, then it's reasonable to infer that there may not have been any horizontal compression or stretch. However:
- If the V-shape extends more steeply, then it could indicate a vertical stretch, but that would also imply that it would go above \( y=3 \) if we have values higher than \( 1 \) which is not the case here.
- If the V-shape is wider or matches the standard \( |x| \), it indicates no compression. Thus we might think about it being vertically translated up higher towards the higher points (like moving \( |x| \) to something like \( |x| + h \) for some \( h \)).
Given that the only reasonable option left would be:
- The parent function was vertically translated up.
Therefore, the correct answer is:
**The parent function was vertically translated up.**
Since the y-axis ranges from 0 to 3 and the function is an upward-facing V-shape, it's likely that the graph is showing a vertical translation, but since it never goes below \( y=0 \), it appears that there has likely been no vertical translation down.
If the graph matches the parent function \( f(x) = |x| \) without any changes in width, then it's reasonable to infer that there may not have been any horizontal compression or stretch. However:
- If the V-shape extends more steeply, then it could indicate a vertical stretch, but that would also imply that it would go above \( y=3 \) if we have values higher than \( 1 \) which is not the case here.
- If the V-shape is wider or matches the standard \( |x| \), it indicates no compression. Thus we might think about it being vertically translated up higher towards the higher points (like moving \( |x| \) to something like \( |x| + h \) for some \( h \)).
Given that the only reasonable option left would be:
- The parent function was vertically translated up.
Therefore, the correct answer is:
**The parent function was vertically translated up.**
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