Question

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

Answer 1

Answer: Option D

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

Step-by-step 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 $h$ 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.