Question

PLEASE HELP!!!!!!!!!!!!

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
I would rlly appreciate it!!! :)

Answer 1

Answer: Option D

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 $h <0$ 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.