SOLUTION: Sketch the graph of the following functions g(x) = (x - 2)^3 + 2

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Question 87017: Sketch the graph of the following functions
g(x) = (x - 2)^3 + 2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the graph of y=x%5E3

+graph%28+500%2C500%2C-10%2C10%2C-10%2C10%2C+x%5E3%29+

Since we have %28x-2%29%5E3 this means we shift the graph 2 units to the right.
So shift the graph 2 units to the right like this:

+graph%28+500%2C500%2C-10%2C10%2C-10%2C10%2C+x%5E3%2C+%28x-2%29%5E3%29+ Graph of y=x%5E3 (red) and y=%28x-2%29%5E3 (green)

Now since we're adding 2 to y=%28x-2%29%5E3 to get y=%28x-2%29%5E3%2B2 this means we shift the graph y=%28x-2%29%5E3 up two units like this

+graph%28+500%2C500%2C-10%2C10%2C-10%2C10%2C+x%5E3%2C+%28x-2%29%5E3%2C+%28x-2%29%5E3%2B2%29+ Graph of y=x%5E3 (red) , y=%28x-2%29%5E3 (green), and y=%28x-2%29%5E3%2B2 (blue)

So the graph of y=%28x-2%29%5E3%2B2 is

+graph%28+500%2C500%2C-10%2C10%2C-10%2C10%2C%28x-2%29%5E3%2B2%29+ Graph y=%28x-2%29%5E3%2B2