SOLUTION: Graph f(x)<= x^2-x-1

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Question 289111: Graph f(x)<= x^2-x-1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Simply graph the polynomial x%5E2-x-1 to get:


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-x-1%29+


Now just shade the ENTIRE region below the curve. This shaded region is the red region shown below:

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+y%3C=x%5E2-x-1%29+


So why did we shade below? Since f(x) is really 'y' and f(x) is less than or equal to x%5E2-x-1, this means that all of the y values that satisfy y%3Cx%5E2-x-1 will be below the curve.