Question

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

Answer 1

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]}