Chapter 3 Graphs and Functions Copyright 2015 2011

Chapter Sections 3. 1 – Graphs 3. 2 – Functions 3. 3 – Linear

§ 3. 2 Functions Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3

Understand Relations Dependent and Independent Variables For an equation in variables x and y,

Recognize Functions Function A function is a relation in which each element in the

Use the Vertical Line Test Graph of Function or Relation The graph of a

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

Understand Function Notation If an equation involving x as the independent variable and y

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Chapter Sections 3. 1 – 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 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3 -2 2

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. Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3 -4 4

Recognize Functions Function A function is a relation in which each element in the domain corresponds to exactly one element in the range. Persons Ages Tom Bob Mark Bill 21 22 25 20 FUNCTION NOT A FUNCTION (Tom can’t be 21 and 22 at the same time) Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3 -5 5

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. Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3 -6 6

Understand 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). When a function is evaluated, a value is substituted into the function. f(x) = 3 x + 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 = 3 x + 2. Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3 -8 8