Question

How does the graph of g(x) = −(x + 3)^4 compare to the parent function of f(x) = x^4

A) g(x) is shifted 3 units to the right and 1 unit up
B) g(x) is shifted 3 units to the right and 1 unit down
C) g(x) is shifted 3 units to the right and reflected over the x-axis.
D) g(x) is shifted 3 units to the left and reflected over the x-axis.

Answer 1

Answer: Option D

g(x) is shifted 3 units to the left and reflected over the x-axis.

Explanation:

If we have a main function
`f (x) = x ^ 4`

And we perform the transformation:

`g (x) = f (x + h) = (x + h) ^ 4`

Then it is fulfilled that:

If
`h> 0` the graph of f(x) moves horizontally h units to the left

If
`h <0` the graph of f(x) moves horizontally h units to the right

If we have a main function
`f (x) = x ^ 4`

And we perform the transformation:

`g (x) = -f(x) = -x ^ 4`

Then it is fulfilled that:

The graph of g(x) is equal to the graph of f(x) reflected on the x axis

In this case we have to:

`g(x) = -(x + 3)^4` and
`f(x) = x^4`

Therefore
`h=3>0` and
`g(x) = -f(x)`

This mean that: g(x) is shifted 3 units to the left and reflected over the x-axis.