7.2 Polynomial Functions and Their Graphs Objectives Identify and describe the important features of the graph of a polynomial function. Use a polynomial function to model real-world data.

Glossary Terms continuous function decreasing function 7.2 Polynomial Functions and Their Graphs Glossary Terms continuous function decreasing function discontinuous function end behavior increasing function leading coefficient local maximum local minimum turning point zero of a function

Rules and Properties Local Maximum and Minimum 7.2 Polynomial Functions and Their Graphs Rules and Properties Local Maximum and Minimum f(a) is a local maximum if f(a) > f(x) for all values of x in an interval around a where x  a. f(a) is a local minimum if f(a) < f(x) for all values of x in an interval around a where x  a.

Rules and Properties Increasing and Decreasing Functions 7.2 Polynomial Functions and Their Graphs Rules and Properties Increasing and Decreasing Functions f is increasing over an interval if f(b) > f(a) where b > a. f is decreasing over an interval if f(b) < f(a) where b > a.

7.2 Polynomial Functions and Their Graphs Key Skills Identify and describe the important features of the graph of a polynomial function. g(x) = x3 – 6x2 + 9x Leading coefficient is positive. Degree is odd. Graph falls on left and rises on right.

7.2 Polynomial Functions and Their Graphs Key Skills Identify and describe the important features of the graph of a polynomial function. g(x) = x3 – 6x2 + 9x increases when x < 1 or x > 3 local max at (1, 4) local min at (3, 0) zeros at 0 and 3 TOC