Comment
The first thing you should do with something like this is to feed it into a program that will graph it for you. A commonly used program on this site is Desmos.
The next thing to do is what you started to do. Fill out a table.
Step One
Get the graph of this function.
I have uploaded 2 graphs. The first one is just a general picture of what the graph looks like. I accepted the constants that Desmos used for the domain and range.
The second graph is a focus on the region around x = - 4 which seems to be quite strange. It almost looks like it's got a vertical line at x = - 4. Actually it just takes very little to move it up the y axis.
Step Two
Make up a table
Before starting to fell out the table, let's make sure you understand how to put this in your calculator. Take a value for x. You used - 4. I'll go to - 3
(-3 + 4) ^(1/3) + 1
(1)^(1/3) + 1
1 this is where you start your calculator.
^ or y^x or x^y Your calculator should have 1 of these keys.
(
1
/
3
)
=
+
1
=
You should get 2
Try another one. This time I'll just give you the answer
x = - 2
y = (-2 + 4)^(1/3) + 1
y = 2.26
x (x + 4)^(1/3) + 1
-3 2
-2 2.36
-1 2.44
0 2.587 This is the y intercept.
Step Three
You were asked for the domain and range
Domain: -infinity < x < plus infinity
Range: - infinity < x < plus infinity
