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Good day students welcome to mathgotserved.com in this clip were going to be learning how to find the end behavior of polynomial functions we're going to get started by taking a look at the something called the leading coefficients test okay the leading coefficient test is something we can use to describe the end behavior of a function now in the charts provided here we can take a look at what the leading coefficient test is if you like to get access to a copy of this document you can visit our website@mathgotserved.com on the algebra two on to the top peak polynomial functions and you will find out this document to download okay so let's see what the leading coefficient test tells us there two is that were looking that's what we identify the leading term will looking at the sign of the leading coefficient is the leading coefficient positive or negative and then we're also looking at the degree of the polynomial okay with a with an ask ourselves is the degree even or is it degree odd to be is on the sign of the leading coefficient and the symmetry of the degree we can determing what the and behavior is so let's take a look at will the chart tells us it tells is that is the degrees even and the leading coefficient is positive then the polynomial function is going to rise to the left and rice to the right if the degree is even and the leading coefficient is negative the opposite happens the polynomial falls to the left and full to the right when you dealing with the leading coefficient test think about even as the same okay and then think about odd as different what I mean by that well if you look at the end behavior of both positive and negative coefficient of and even degree polynomial you find out that either the rice together already full together that's the behavior off polynomial's with even degrees now let's take a look at polynomial's we ought degrees in the degree is odd and the leading coefficient is positive the polynomial is going to fall to the left in rice to the right in the degrees in the leading coefficient is negative the reverse happens is rises to the left and false to the right if you compared the end behavior of the even degree polynomials in a degree polynomials you see that the our degree polynomials going different directions to the left and to the right breast that even degree polynomial is going to send direction to the left and right think about the even degree polynomial at happy or sad these than the sign writing so happy Om is to positive leading coefficients and said he's were negative leading coefficients the best is something to keep in mind before we take a look at some examples we're going to review how to write the and behavior of functions okay so the notation is very important now let's take a look at the for cases now let's assume that you have a situation where the polynomial is rising to the right okay so this is right right here in this is the right is in the direction of the x-axis us write it again and Om so rights in the direction of the x-axis and then rise is when he had upwards aright EV go on forever you ahead and towards infinity equal to the rights forever unit heading towards infinity EV polynomial function is rising to the rights we can write it as rise rises to the right how do you express this using mathematical okay notation so this is FO backs in this is X it will polynomial rises to the right is simply means that the function or why is approaching this out of is approaching approaches infinity our lives X approaches X on sorry X approaches infinity so Om rising to the right basically means that F of X the function is rising going of two infinity as he had to or is the right direction positive infinity in the horizontal orientation okay so in mathematical notation rising to the right is written as F of X approaches infinity as X approaches infinity now let's take a look at the other scenario what if you were falling to the right so we have positive infinity on the right and 4X and we have negative infinity for the function why equals F of X this means falls okay so in this case right here so this is case one in case to know what you have is out the polynomial falls to the right okay so the polynomial falls to the right how do you write that using mathematical notation fall basically means of the function is approaching negative infinity that's what you have way of the bottom what we hear the function approaches negative infinity as X goes to the rights which is infinity our rights of you have an end behavior of this orientation to the right this is how you write it F of X approaches negative infinity as X approaches infinity our right let's take a look at the case number three what if you are in

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