Explain how to use the Leading Coefficient Test to determine

*Explain how to use the Leading Coefficient Test to determine the end behavior of a function. Write at least three lines and include in your discussion two cases for odd exponents and two cases for even exponents.

Solution

Leading Coefficient Test: The leading coefficient of a polynomial is used to determine the end behaviour.

f(x) = x^4 +5x +3 .Here leading term is x^4 and leading coefficient is 1

Case1: leading term is odd:If n is odd and the leading coefficient is positive, the graph falls to the left and rises to the right: eg: f(x) = 5x^3 -2x^2 +6

If n is odd and the leading coefficient  is negative, the graph rises to the left and falls to the right.

eg: -7x^5 +x^ -7

Case 2 : If n is even and the leading coefficient  is positive, the graph rises to the left and to the right.

eg: x^4 +2x^2 +3

If n is even and the leading coefficient, is negative, the graph falls to the left and to the right.

eg: -x^6 +3