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...

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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:**