Copyright © 2005 Pearson Education, Inc.

Chapter 9 Copyright © 2005 Pearson Education, Inc.

Functions A function describes how a dependent variable changes with respect to one or more independent variables. When there are only two variables, we often summarize them as an ordered pair with the independent variable first: (independent variable, dependent variable) We say that the dependent variable is a function of the independent variable. If x is the independent variable and y is the dependent variable, we write the function as y = f(x) Copyright © 2005 Pearson Education, Inc.

Representing Functions 9-A Representing Functions There are three basic ways to represent functions. Data Table Draw a picture or graph Write an equation Copyright © 2005 Pearson Education, Inc.

Domain and Range The domain of a function is the set of values that both make sense and are of interest for the independent variable. The range of a function consists of the values of the dependent variable that correspond to the values in the domain. Copyright © 2005 Pearson Education, Inc.

Hours of Daylight as a Function Here is a simple example of a periodic function that could be used as an introduction into the concepts of domain, range, independent and dependent variables. Copyright © 2005 Pearson Education, Inc.

9-B Linear Functions Walk through with your class several practical examples the four types of slope (positive, negative, zero, undefined). One motto for linear applications: “Don’t give up hope, find the slope!” Copyright © 2005 Pearson Education, Inc.

Slope-Intercept Form of a Line 9-B Slope-Intercept Form of a Line y = mx + b y = 3x – 7 refers to a line whose slope is equal to 3 and a y-intercept of -7. Copyright © 2005 Pearson Education, Inc.

Exponential Functions Copyright © 2005 Pearson Education, Inc.

Two Ways to Describe Exponentials Remind students that Q(sub-not) is simply the initial value and Q is the new value that we referred to back in Chapter 8. Copyright © 2005 Pearson Education, Inc.

Changing Rates of Change The thinking about . . . box on (page 534) is a great way to help students at least have a rough appreciation and understanding for the underpinnings of the calculus. Copyright © 2005 Pearson Education, Inc.