Question
Interpret the key features of the graph. What type of transformation occurred from the parent function?
(1 point)
Responses
This is a vertical stretch of the parent function y=x2
due to the changes in the x-intercept.
This is a vertical stretch of the parent function y equals x squared due to the changes in the x- intercept.
This is a vertical stretch of the parent function y=x2
due to the changes in the y-coordinates of each point.
This is a vertical stretch of the parent function y equals x squared due to the changes in the y -coordinates of each point.
This is a vertical stretch of the parent function y=x2
due to the changes in the x-coordinates of each point.
This is a vertical stretch of the parent function y equals x squared due to the changes in the x -coordinates of each point.
This is a vertical stretch of the parent function y=x2
due to the changes in the y-intercept.
(1 point)
Responses
This is a vertical stretch of the parent function y=x2
due to the changes in the x-intercept.
This is a vertical stretch of the parent function y equals x squared due to the changes in the x- intercept.
This is a vertical stretch of the parent function y=x2
due to the changes in the y-coordinates of each point.
This is a vertical stretch of the parent function y equals x squared due to the changes in the y -coordinates of each point.
This is a vertical stretch of the parent function y=x2
due to the changes in the x-coordinates of each point.
This is a vertical stretch of the parent function y equals x squared due to the changes in the x -coordinates of each point.
This is a vertical stretch of the parent function y=x2
due to the changes in the y-intercept.
Answers
Answered by
GPT-4o mini
To interpret the key features of a graph that shows a transformation of the parent function \( y = x^2 \), we need to look specifically at how the graph has changed and what type of transformation has occurred.
A vertical stretch of the parent function occurs when the output values (y-coordinates) of the function are multiplied by a factor greater than 1. This will make the parabola narrower but does not affect the x-coordinates directly; instead, it scales the y-coordinates of the points on the graph.
Given the options provided:
1. **Vertical stretch due to changes in x-intercept**: This is incorrect since the x-intercepts don't directly determine whether there's a vertical stretch.
2. **Vertical stretch due to changes in y-coordinates**: This is correct. A vertical stretch indeed refers to changes in the y-coordinates of the graph.
3. **Vertical stretch due to changes in x-coordinates**: This is incorrect, as changes in x-coordinates do not contribute to vertical stretching.
4. **Vertical stretch due to changes in y-intercept**: This is not representative of vertical stretching; the y-intercept may change but does not define a vertical stretch.
Based on this reasoning, the correct interpretation would be:
**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 of the parent function occurs when the output values (y-coordinates) of the function are multiplied by a factor greater than 1. This will make the parabola narrower but does not affect the x-coordinates directly; instead, it scales the y-coordinates of the points on the graph.
Given the options provided:
1. **Vertical stretch due to changes in x-intercept**: This is incorrect since the x-intercepts don't directly determine whether there's a vertical stretch.
2. **Vertical stretch due to changes in y-coordinates**: This is correct. A vertical stretch indeed refers to changes in the y-coordinates of the graph.
3. **Vertical stretch due to changes in x-coordinates**: This is incorrect, as changes in x-coordinates do not contribute to vertical stretching.
4. **Vertical stretch due to changes in y-intercept**: This is not representative of vertical stretching; the y-intercept may change but does not define a vertical stretch.
Based on this reasoning, the correct interpretation would be:
**This is a vertical stretch of the parent function \( y = x^2 \) due to the changes in the y-coordinates of each point.**