Question

Describe the graph of the function f(x) = x^3 − 18x^2 + 101x − 180. Include the y-intercept, x-intercepts, and the end behavior in your desription.

Answer 1

The "y-intercept" is the notable point of the function where the "x" value is zero, therefore, we will take the function and replace all the "x's" with "0's" and that will allow us to know where in the y-axis the point is situated:

f(0)=(0)³−18(0)²+101(0)−180
f(0) = -180

The "x" interception is a little more complex, but very linear concept, but these notable or notable points have the definition of nullifying the function, meaning that we want to know the values of "x" that make the whole function equal zero:

x³−18x²+101x−180=0

x³−18x²+101x−180=0when factored we get(x−4)(x−5)(x−9)=0
we then let each bracket=0 since they are product of each other..
(x−4)=0(x−5)=0(x−9)=0..sox=4x=5x=9