Question

To graph the function g(x)=-(x-4)^3, start with the graph f(x)=x^3 then make which of the following changes?

A. Shift the graph of left by 4 units.
B. Shift the graph of right by 4 units.
C. Shift the graph of up by 4 units.
D. Shift the graph of down by 4 units.
E. Reflect the graph of over the -axis.
F. Reflect the graph of over the -axis.
G. Stretch the graph of horizontally.
H. Stretch the graph of vertically.

Answer 1

(there can be more than one answer)

Answer 2

f(x - h) is a horizontal shift applied to f(x)
If h is positive it's to the right. If h is negative it's to the left.

-f(x) compared to f(x) is a reflection over the x axis.

Answer 3

So what letter answer(s) is that?

Answer 4

1. I gave you enough info for you to figure it out.
2. You didn't give enough info for me to figure it out.
Your choices E and F are the same. There is something missing.

Answer 5

E is suppose to be y axis and F is suppose to be x axis. My apologies

Answer 6

And the answer you gave me appears wrong that's why I was double checking the letters.

Answer 7

Ok. I'm back now.
The problem tells you to start with f(x) = x^3.
You want to graph g(x) = -(x - 4)^3, so you compare it to f(x) = x^3.

One thing you notice is that g(x) has (x - 4)^3 instead of x^3.
This means that x has been replaced by x - 4.
According to my explanation above, when x is replaced by x - h,
you get a horizontal shift.
In this case, since x - h = x - 4, that means h = 4.
4 is a positive number, so that means the graph of g(x) has a shift of 4 units to the right.

Now let's deal with the negative sign in front of -(x - 4)^3.
Notice I wrote above that when -f(x) is compared to f(x),
this means a reflection over the x-axis.
If you start with f(x) = x^3, and you only shift the graph 4 units to the right,
you get h(x) = (x - 4)^3.
By introducing the negative sign, as in g(x) = -(x - 4)^3, that means you are also reflecting the graph over the x-axis.

That means that g(x) compared to f(x) has had two transformations done.
It has shifted 4 units to the right, and it has been reflected over the x-axis.

Answer 8

Just one note.
When you copy a problem and post it, you should check that the problem has been copied correctly. There are symbols used in problems that are not regular characters and will not be copied with a simple copy and paste operation. If you look at every choice you wrote above, notice that everyone of them has missing info.
Every choice starts with "Shift the graph of ", but it then does not state which graph it's referring to. This is because the function itself was written in some type of image that was not copied by copy and paste. The same thing happened with the choices that are reflections over the x- and y-axes, where the letters x and y were not copied.