SOLUTION: How do I determine the end behaviour of {{{ f(x)= x^7-18x^5+81x^3 }}}, and finding the zeroes of f, the multiplicity and the behaviour of the graph corresponding to the x-intercept

Question 997402: How do I determine the end behaviour of , and finding the zeroes of f, the multiplicity and the behaviour of the graph corresponding to the x-intercept?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
x7-18x^5+81x^3
First, the end behavior. As x becomes large, the x^7 term drives the result. As x goes to + infinity, so does the function. As x goes to negative infinity, so goes the function.
factor out x^3
x^3(x^4-18x^2+81)=0
x^3(x^2-9)^2
X^3(x+3)^2(x-3)^2=0
graph should go from minus infinity and bounce at -3, going down and back up to 0 above the y-axis and then back down to +3, where it bounces and goes to positive infinity. Multiplicity of root -3 is 2, of root 0 is 3, and root +3 is 2.

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