A V shaped line passes through 7 plotted points on a coordinate plane with x-axis ranging from negative 9 to 9 in increments of 1 and y-axis ranging from negative 11 to 11 in increments of 1. An upward open parabola passes through 5 plotted points on a coordinate plane with x-axis ranging from negative 12 to 12 in increments of 2 and y-axis ranging from negative 6 to 18 in increments of 2.

Question

A V shaped line passes through 7 plotted points on a coordinate plane with x-axis ranging from negative 9 to 9 in increments of 1 and y-axis ranging from negative 11 to 11 in increments of 1.	 An upward open parabola passes through 5 plotted points on a coordinate plane with x-axis ranging from negative 12 to 12 in increments of 2 and y-axis ranging from negative 6 to 18 in increments of 2.
Describe the similarities in the transformations of each of the function graphs from their parent function.

(1 point)
Responses

The intercepts of both graphs have changed as a result of the transformation.
The intercepts of both graphs have changed as a result of the transformation.

No changes have been made from the parent function.
No changes have been made from the parent function.

Both graphs have been vertically compressed.
Both graphs have been vertically compressed.

Both graphs have been vertically stretched.
Both graphs have been vertically stretched.

GPT-4o mini · Answer

To determine the similarities in the transformations of the given function graphs from their parent functions, we'll first identify the parent functions for both the V-shaped line and the upward-opening parabola.

The parent function of the V-shaped line is typically \( y = |x| \).
The parent function of the upward-opening parabola is typically \( y = x^2 \).

Intercepts: The intercepts of both graphs have likely changed from their parent functions due to the transformations (such as translations or reflections) that would move the vertex or roots of the functions.
No Changes: This option is not applicable because both graphs have been transformed to fit the given points.
Vertical Compression: This would suggest that the graphs have been shrunk towards the x-axis, which does not seem to apply based on the provided information without specific transformation parameters.
Vertical Stretch: This would indicate that the graphs have been stretched away from the x-axis, but there's no evidence or specific transformation mentioned in the question supporting this claim.

Given these considerations, the most appropriate response from the options presented is:

The intercepts of both graphs have changed as a result of the transformation.

This reflects that both graphs have undergone transformations affecting their intercepts, differentiating them from their respective parent functions.