# Thread: [SOLVED] End Behavior of a function

1. ## [SOLVED] End Behavior of a function

I am suppose to find the end behavior of

[(u-1)(u-2)^2(u-3)^3)/((u-1)^3(u-2)^2(u-3))

I looked at my calculator and what I can determine is
as x approaches negative infinity f(x) approaches 1 and as
x approaches positive infinity f(x) approaches 1

am I doing this right, or is there something I am missing??

Thanks

2. Originally Posted by mandy123
I am suppose to find the end behavior of

[(u-1)(u-2)^2(u-3)^3)/((u-1)^3(u-2)^2(u-3))

I looked at my calculator and what I can determine is
as x approaches negative infinity f(x) approaches 1 and as
x approaches positive infinity f(x) approaches 1

am I doing this right, or is there something I am missing??
If you were to multiply numerator and denominator out, they would be polymnomials of degree 6 with leading term $u^6$ (you don't have to actually multiply to see that). If you divide both numerator and denominator by $u^6$, each will be 1+ terms with u in the denominator. As u goes to either positive or negative infinity the terms with u in the denominator go to 0 so, yes, the whole fraction goes to 1/1= 1.