Question
Interpret the key features of the graph. What type of transformation occurred from the parent function?
(1 point)
Responses
A. This is a vertical stretch of the parent function y=x2 due to the changes in the y-coordinates of each point.
B. This is a vertical stretch of the parent function y=x2 due to the changes in the y-intercept.
C. This is a vertical stretch of the parent function y=x2 due to the changes in the x-coordinates of each point.
D. This is a vertical stretch of the parent function y=x2 due to the changes in the x-intercept.
(1 point)
Responses
A. This is a vertical stretch of the parent function y=x2 due to the changes in the y-coordinates of each point.
B. This is a vertical stretch of the parent function y=x2 due to the changes in the y-intercept.
C. This is a vertical stretch of the parent function y=x2 due to the changes in the x-coordinates of each point.
D. This is a vertical stretch of the parent function y=x2 due to the changes in the x-intercept.
Answers
Answered by
GPT-4o mini
To determine the correct interpretation of the transformation from the parent function \(y = x^2\), we need to consider how vertical stretches impact the graph.
A vertical stretch occurs when the output (y-coordinates) of the function is multiplied by a factor greater than 1. This means that for each x-coordinate, the corresponding y-coordinate becomes larger positive values, making the graph appear "taller" or more "stretched" vertically.
Let's analyze the response options:
A. This suggests that the y-coordinates are changed, which is consistent with the idea of a vertical stretch.
B. The y-intercept is specific and wouldn't denote a general vertical stretch; it could just be stating a specific point rather than a transformation.
C. Changes in the x-coordinates pertain to horizontal stretching or shifting, which is not what a vertical stretch involves.
D. Similar to option B, the x-intercept changes refer to a specific point rather than indicating a transformation.
Given this analysis, the most appropriate response is:
**A. This is a vertical stretch of the parent function y=x^2 due to the changes in the y-coordinates of each point.**
A vertical stretch occurs when the output (y-coordinates) of the function is multiplied by a factor greater than 1. This means that for each x-coordinate, the corresponding y-coordinate becomes larger positive values, making the graph appear "taller" or more "stretched" vertically.
Let's analyze the response options:
A. This suggests that the y-coordinates are changed, which is consistent with the idea of a vertical stretch.
B. The y-intercept is specific and wouldn't denote a general vertical stretch; it could just be stating a specific point rather than a transformation.
C. Changes in the x-coordinates pertain to horizontal stretching or shifting, which is not what a vertical stretch involves.
D. Similar to option B, the x-intercept changes refer to a specific point rather than indicating a transformation.
Given this analysis, the most appropriate response is:
**A. This is a vertical stretch of the parent function y=x^2 due to the changes in the y-coordinates of each point.**