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QUESTION

# How do you write the notation for end behavior?

You write the notation using the limit notation.

So first of all before you write the limit notation you need to look at the degree of the polynomial and determine if the graph is odd or even.

Let's take a look at the below polynomial

f(x)=x^3-3x^2-x+2

The degree of the polynomial is 3 which is odd number. So the rule here is that if the degree is odd then the will be opposite and if it is even it will be even.

 lim f(x)_(x -> ∞)=∞

 lim f(x)_(x -> -∞)=-∞

The notation is read as, "The limit of f(x) as x goes to [infinity] is ...[infinity]"

Here is a graph of a the function and as you can see the goes the opposite direction. graph{x^3-3x^2-x+2 [-10, 10, -5, 5]}

Now let's do even one. x^2+1

The degree is 2 so the function is even. and you write the limit function as below.

 lim f(x)_(x -> ∞)=∞

 lim f(x)_(x -> -∞)=∞

Let's graph the function and you can see the in the parabola so it doesn't matter what number you pick for x it will always be positive thus the end behavior will go the same direction. graph{x^2+1 [-25.66, 25.65, -12.84, 12.83]}