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

c: g(x) is shifted 3 units to the right and reflected over the x-axis

Answer 2

Answer: Option D

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

Explanation:

If we have a function f(x) and make a transformation of the form:

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

Then it is true that:

If
`h> 0` the graph of g(x) is equal to the graph of f(x) displaced h units to the left

If
`h<0` the graph of g(x) is equal to the graph of f(x) displaced h units to the right

Also if we have a function f(x) and perform a transformation of the form:

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

Then it is true that:

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

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

So

`g(x) = -f(x+3)`

Then
`h = 3> 0`. Therefore the graph of g(x) is equal to the graph of f(x) displaced 3 units to the left and reflected on the x axis

The answer is the option D