Question

If the cube root parent function is horizontally stretched by a factor of 4, then translated 5 units right and 3 units up, write an equation to represent the new function?

Answer 1

Answer:

The cube root parent function:

• f(x) = $\sqrt[3]{x}$

Horizontally stretched by a factor of 4:

• g(x) → f(1/4x) = $\sqrt[3]{1/4x}$

Translated 5 units right:

• h(x) → g(x - 5) = $\sqrt[3]{1/4x - 5}$

Translated 3 units up:

• k(x) → h(x) + 3 = $\sqrt[3]{1/4x - 5} + 3$