Question

Graph the function  f(x)=x^3  and g(x)=x^3+1.

Accepted Answer

To graph the function f(x)=x^3 , assign values to x and solve for y.
x=-3  ,  y=x^3=(-3)=-27
x=-2  ,  y=(-2)^3=-8
x=-1  ,  y=(-1)^3=-1
x=0   ,  y=0^3=0
x=1   ,  y=1^3=1
x=2   ,  y=2^3=8
x=3   ,  y=3^3=27
Then, plot the points (-3,-27) , (-2,-8) , (-1,-1) , (0,0) , (1,1) , (2,8) , (3,27). And connect them.
Hence, the graph of the function f(x)=x^3 is:

To graph for the second function g(x)=x^3+1 , notice that we only add the previous function with 1 to get the second function g(x).
So, we may express the second function as:
g(x)=x^3+1
g(x)=f(x) + 1
Since we already have the graph of f(x),  to graph g(x), apply transformation of function.
Since g(x) is in the form  y_2 = y_1+k , do vertical shift. So, move the graph of f(x) 1 unit up to get the graph of g(x).
Thus, the graph of the function g(x) =x^3+1 is:

Answer

Adding 1 to the function moves the whole thing up. Similarly, subtracting from the function moves the whole thing down. If we were to add the 1 inside the x for instance (x+1)^3; the whole graph moves left one. If were to subtract 1, the whole graph moves to the right. 
The black line is your parent function f(x) = x^3. The red line is f(x) = (x^3) + 1. 
If were to look at other translations: 
The red line is (x+1)^3 and the orange line is (x-1)^3. 
Remembering how translations work will help you easily draw graphs.

Math

Graph the function `f(x)=x^3` and `g(x)=x^3+1.`

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