1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-1 Graphs and Functions Chapter 3

2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter – Graphs 3.2 – Functions 3.3 – Linear Functions: Graphs and Applications 3.4 – The Slope-Intercept Form of a Linear Equation 3.5 – The Point-Slope Form of a Linear Equation 3.6 – The Algebra of Functions 3.7 – Graphing Linear Inequalities Chapter Sections

3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-3 § 3.2 Functions

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-4 Understand Relations Dependent and Independent Variables For an equation in variables x and y, if the value of y depends on the value of x, then y is the dependent variable and x is the independent variable. Relation, Domain, Range For an equation in variables x and y, if the value of y depends on the value of x, then y is the dependent variable and x is the independent variable.

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-5 Recognize Functions Persons Tom Bob Mark Bill Ages Persons Tom Bob Mark Bill Ages FUNCTION NOT A FUNCTION (Tom can’t be 21 and 22 at the same time) Function A function is a relation in which each element in the domain corresponds to exactly one element in the range.

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-6 Use the Vertical Line Test Graph of Function or Relation The graph of a function or relation is the graph of its set of ordered pairs. Vertical Line Test If a vertical line can be drawn so that it intersects a graph at more than one point, then the graph does not represent a function. If a vertical line cannot be drawn so that it intersects a graph at more than one point, then the graph represents a function.

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-7 Vertical Line Test FUNCTION NOT A FUNCTION FUNCTION

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-8 Understand Function Notation When a function is evaluated, a value is substituted into the function. f(x) = 3x + 2 f(1) = 3(1) + 2 = 5 Therefore, when x is 1, y is 5. The ordered pair (1, 5) appears on the graph of y = 3x + 2. Function Notation If an equation involving x as the independent variable and y as the dependent variable defines a function, we say y is a function of x and we write y = f(X).