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^3+7x^2−x+9

Accepted Answer

Welcome back. I'm so glad you're here. We are given the function F of X equals seven X cubed plus two X squared minus three X plus 11. And we are asked to determine the end behavior of the graph using the leading coefficient test. Alright, first step is to make sure that all of our terms are in order, we want them in descending order of their variables exponents. And in this case there are 3210. Great. In the next step is we just look at this first term here. Seven ex cute. And we're going to ask ourselves two questions. The first question looks at the exponent, we look at the exponent and ask ourselves is the exponent odd or even so is three odd or even? Well three is odd. So we're going to proceed with the odd column. The next question we ask ourselves is about the terms coefficient. In this case the coefficient is seven. We're going to ask ourselves is seven positive or negative and it is positive. So we recall from previous lessons that in this column, when we have a positive coefficient with an odd exponent, then the function will fall to the left and then something happens in the middle and then it rises to the right. We look at our answer choices and that matches with answer choice. A well done. We'll catch 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^3+7x^2−x+9

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