Question

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

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

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

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

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

Answer 1

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

Reason: A parent function is the simplest form of a family (e.g., y = x^2 for quadratics). Applying translations, reflections, stretches/shrinks, and scalings produces every other member of that family. The other statements are false (translations are not limited by position, there is typically one parent per family, and a parent may undergo zero, one, or more transformations).