Let us under stand the basics of determining the end behavior of a graph , by just analyzing the degrees and coefficient of a polynomial.Please refer to the image we have shared with this for a better understanding also.

The rule is bifurcated in two broad category and and two sub category in them.

Category .

The nature of degree (Even / Odd )

Subcategory .

The coefficient of term containing degree ( Negative/Positive )

Rule 1 :

Degree : Even

If coefficient is

Rule 1(a) : Positive ⇒Both ends are towards +ve infinity

Rule 1(b) : Negative⇒Both ends are towards -ve infinity

Rule 2 :

Degree : Odd

If coefficient is

Rule 2(a) : Positive ⇒ Left ends is -ve infinity and Right end is +ve infinity

Rule 2(b) : Negative ⇒ Left ends is +ve infinity and Right end is -ve infinity

Let us see our function f(x) = $-2x^3 + 3x$ now

Here

Degree is 3 which is Odd

Its coefficient is (-2) which is negative

Hence we go to rule 2(b)

That is the Left ends is +ve infinity and Right end is -ve infinity. however both tends to be infinity.

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3 years ago