SOLUTION: sketch the graph of the polynomial function. f(x)=(x+1)^3+4

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: sketch the graph of the polynomial function. f(x)=(x+1)^3+4      Log On


   

Question 113828: sketch the graph of the polynomial function.
f(x)=(x+1)^3+4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

In order to graph y=%28x%2B1%29%5E3%2B4, first graph its parent equation y=x%5E3
+graph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E3%29 Graph of y=x%5E3


Now add 4 to the whole equation to shift the graph up 4 units to get the new graph of y=x%5E3%2B4 which looks like
+graph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2Cx%5E3%2Cx%5E3%2B4%29 Graph of y=x%5E3(red) and y=x%5E3%2B4(green)

Now replace x with x+1 to get y=%28x%2B1%29%5E3%2B4 which shifts the graph to the left 1 unit
So our new graph looks like


+graph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2Cx%5E3%2Cx%5E3%2B4%2C%28x%2B1%29%5E3%2B4%29 Graph of y=x%5E3(red), y=x%5E3%2B4(green), and Graph of y=%28x%2B1%29%5E3%2B4


So our final graph y=%28x%2B1%29%5E3%2B4 alone looks like

+graph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%28x%2B1%29%5E3%2B4%29 Graph of y=%28x%2B1%29%5E3%2B4