In Exercises 19–24, use the Leading Coefficient Test to determine...

Question

In Exercises 19–24, use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. f(x)=−5x^4+7x^2−x+9

Accepted Answer

Welcome back. I'm so glad you're here. We are given a function F of X equals negative nine X to the fourth plus nine X squared plus two X plus 11. And we are to determine the end behavior of this graph Using the leading coefficient test. Well, the first thing we need to ensure is that all of our terms are in order. We want them in descending order for each variables exponents. So 4-1, 0. These are already in order. Great. So now for the leading test, we are just going to focus on this first term, the one with the leading coefficient, so in this case negative nine X to the fourth. And we ask ourselves two questions. The first question is looking at the exponents. So to the fourth here and we ask ourselves is the exponent odd or even so as for odd or even for is even so we're going to focus on the even column. And the next thing that we're going to look at is the coefficient. And we're going to ask ourselves is the coefficient positive or negative and negative? Nine that's negative. So we're going to look at the negative column here. And by definition, we know from previous lessons that when we have an even exponent with a negative leading coefficient, we're going to have a graph that falls to the left and then something happens in between and then it will fall to the right as well. We look at our answer choices and this matches with answer choice. D Well done. We'll catch you on the next one

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In Exercises 19–24, use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. f(x)=−5x^4+7x^2−x+9