Polynomials End Behavior of the Graph End behavior

Polynomials: End Behavior of the Graph "End behavior" of the graph of a polynomial refers to the behavior of the function values (y-values) as values of the independent variable, x, increase or decrease without bound. right end Example: In the polynomial shown 10 graphed, the polynomial rises at the 8 y 6 right end, since as x increases 4 without bound, the function values x x 2 (y-values) increase without bound. -20 -10 0 10 20 -2 The polynomial falls at the left end, -4 -6 since as x decreases without bound, y -8 the function values (y-values) -10 left end decrease without bound. Table of Contents

Polynomials: End Behavior of the Graph The "End behavior" of the graph of a polynomial is determined only by its degree and leading coefficient (l. c. ). degree l. c. End Behavior even positive rises on both ends even negative falls on both ends odd positive falls on left end, rises on right end odd negative rises on left end, falls on right end Table of Contents Slide 2

Polynomials: End Behavior of the Graph Try: Without graphing, describe the end behavior of the polynomial, P(x) = 3 x 6 – 2 x 5 + 9 x 3 – 4 x + 8. The graph of the polynomial rises on both ends. Try: Without graphing, describe the end behavior of the polynomial, P(x) = - x 5 + 2 x 4 + 3 x 2 – x + 1. The graph of the polynomial rises on the left and falls on the right. Try: Without graphing, describe the end behavior of the polynomial, P(x) = - x 10 + x 7 + 5 x 4 – x 2 + 3 x. The graph of the polynomial falls on both ends. Table of Contents Slide 3

Polynomials: End Behavior of the Graph Table of Contents