End Behaviour of Polynomial Function

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We know End behaviour can refers to the behaviour of a graph, like it approaches either negative infinity or positive infinity. We
know end behaviour of a polynomial function is determinate by degree of the function and leading coefficient.

If the degree of the polynomial is Even and leading coefficient is positive then

F(x) -> ∞, as x -> -∞ and also F(x) ->∞ as x -> +∞

If the degree of the polynomial is Even and leading coefficient is negative then

F(x) -> -∞, as x -> -∞ and also F(x) -> -∞ as x -> +∞

If the degree of the polynomial is Odd and leading coefficient is positive then

F(x) -> ∞, as x ->∞ and also F(x) ->-∞ as x -> -∞

Example 1: Find the end behaviour of the function x4- 4x3+3x+25

Solution: The given function is F(x) = x4- 4x3+3x+25

The degree of this function is 4, its even number

We can see the leading coefficient,

That is positive.

So the end behaviour is

F(x) -> + ∞, as x -> -∞

F(x) -> + ∞, as x -> ∞

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