Answer:
[tex]g(x)=(x-3)^4-6[/tex]
Step-by-step explanation:
The parent function is [tex]f(x)=x^4[/tex].
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:
[tex]g(x)=f(x-3)-6[/tex]
[tex]\implies g(x)=(x-3)^4-6[/tex]
