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