Question

Which of the following statements shows that parent functions can create all other functions in a function family?(1 point)
Responses

Parent functions can only undergo a vertical translation if they are above the x-axis.
Parent functions can only undergo a vertical translation if they are above the x -axis.

A parent function must undergo at least two transformations to create other functions within the family.
A parent function must undergo at least two transformations to create other functions within the family.

Parent functions can be translated, reflected, and/or dilated to create all functions within a family.
Parent functions can be translated, reflected, and/or dilated to create all functions within a family.

Each function family has two parent functions to create all of the functions in the function family.

Answer 1

The statement that best shows that parent functions can create all other functions in a function family is:

**"Parent functions can be translated, reflected, and/or dilated to create all functions within a family."**

This statement indicates that through transformations—such as translations, reflections, and dilations—parent functions can generate the entire set of functions within a particular family.