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

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lemjay | High School Teacher | (Level 3) Senior Educator

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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:

 

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Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

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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. 

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