Question

For the linear parent function, f(x)=x, a reflection over the x-axis and a reflection over the y-axis produce the same transformed function. However, for the quadratic parent function, f(x)=x ^2, the transformed functions differ. Expain briefly.

Answer 1

For the linear parent function, a reflection over the x-axis and the y-axis produce the same transformed function. However, for the quadratic parent function, the reflections result in different transformed functions.

Step-by-step explanation:

Transformations of Parent Functions

For the linear parent function, f(x)=x, a reflection over the x-axis and a reflection over the y-axis produce the same transformed function. This is because the graph of the linear function remains unchanged when reflected over either axis. Therefore, the transformed function is still f(x)=x.

On the other hand, for the quadratic parent function, f(x)=x^2, the transformed functions differ when reflected over the x-axis and the y-axis. When reflected over the x-axis, the graph of f(x) becomes f(x)=-x^2, resulting in a downward opening parabola. When reflected over the y-axis, the graph becomes f(x)=-x^2, which is still a parabola but with a different orientation.