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.

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

And we perform the transformation:

Then it is fulfilled that:

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

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

If we have a main function

And we perform the transformation:

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:

and

Therefore and

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

b) 1/3 * 1/5

step-by-step explanation:

each smallest part is 1/15 since the written one is 1/5 and it's divided by 3 equal parts. (1/5 )/3 = 1/15 = 1/3 * 1/5