Question

Write a function g with the parent function f(x) = x4 that has a vertex at (3, -6).

Answer 1

Answer:

$g(x)=(x-3)^4-6$

Step-by-step explanation:

The parent function is $f(x)=x^4$.

We want to transform this function so that its vertex will move from the origin to (3,-6).

In other words, we translate the parent function 3 units to the right and 6 units down,

Let g(x) be the new function then:

$g(x)=f(x-3)-6$

$\implies g(x)=(x-3)^4-6$