SOLUTION: graph the function g(x)=(x-1)to the 3rd pwr

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Question 316367: graph the function g(x)=(x-1)to the 3rd pwr
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

In order to graph y=%28x-1%29%5E3, we need to plot a few points.


To get points in the form of (x,y), we need to find corresponding 'y' values to given 'x' values.


Let's find the y value when x=-1 note: you can start at any x value.


y=%28x-1%29%5E3 Start with the given equation.


y=%28-1-1%29%5E3 Plug in x=-1.


y=%28-2%29%5E3 Subtract.


y=-8 Cube -2 to get -8.


So if x=-1, then y=-8 which gives us the point (-1,-8).


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Let's find the y value when x=-0.5


y=%28x-1%29%5E3 Start with the given equation.


y=%28-0.5-1%29%5E3 Plug in x=-0.5.


y=%28-1.5%29%5E3 Subtract.


y=-3.375 Cube -1.5 to get -3.375.


So if x=-0.5, then y=-3.375 which gives us the point (-0.5,-3.375).


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Let's find the y value when x=0.5


y=%28x-1%29%5E3 Start with the given equation.


y=%280.5-1%29%5E3 Plug in x=0.5.


y=%28-0.5%29%5E3 Subtract.


y=-0.125 Cube -0.5 to get -0.125.


So if x=0.5, then y=-0.125 which gives us the point (0.5,-0.125).


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Let's find the y value when x=1


y=%28x-1%29%5E3 Start with the given equation.


y=%281-1%29%5E3 Plug in x=1.


y=%280%29%5E3 Subtract.


y=0 Cube 0 to get 0.


So if x=1, then y=0 which gives us the point (1,0).


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Let's find the y value when x=2


y=%28x-1%29%5E3 Start with the given equation.


y=%282-1%29%5E3 Plug in x=2.


y=%281%29%5E3 Subtract.


y=1 Cube 1 to get 1.


So if x=2, then y=1 which gives us the point (2,1).


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Let's find the y value when x=3


y=%28x-1%29%5E3 Start with the given equation.


y=%283-1%29%5E3 Plug in x=3.


y=%282%29%5E3 Subtract.


y=8 Cube 2 to get 8.


So if x=3, then y=8 which gives us the point (3,8).


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Now let's make a table of the values we just found.


Table of Values:





xy
-1-8


-0.5-3.375


0.5-0.125


10


21


38

Now let's plot the points:




Graph:


Now draw a curve through all of the points to graph y=%28x-1%29%5E3:


Graph of y=%28x-1%29%5E3