Question 997402
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.
{{{graph(300,200,-10,10,-1000,1000,x^7-18x^5+81x^3)}}}