If you have a polynomial where the leading coefficient is positive and the degree is odd, what is the end behavior?

1 Answer
Shwetank Mauria
Feb 17, 2017

As #x->-oo#, #y->-oo# and as #x->oo#, #y->oo# and curve cuts #x#-axis at the zeros of the function #y=f(x)#

Explanation:

In a polynomial say #y=f(x)#, (#f(x)# being a polynomial), where the leading coefficient is positive and the degree is odd,

this means that as #x->-oo#, as the degree is odd, #y->-oo#

and as #x->oo#, as the degree is odd, #y->oo#

Further in between the curve will cut the #x#-axis at all the zeros of the function #y=f(x)#

For example let #y=(x-2)^2(x+3)(x-5)(x+4)#

Here we observe the above behavior and it cuts #x#-axis at #{-4,-3,2,5}#
graph{(x-2)^2(x+3)(x-5)(x+4) [-10, 10, -360, 300]}

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