Download Chapter 3-2

Chapter 3
Graphs and
Functions
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 3-1
1
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
§ 3.2
Functions
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 3-3
3
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
Persons
Ages
Tom
Bob
Mark
Bill
21
22
25
20
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
Vertical Line Test
FUNCTION
FUNCTION
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
NOT A
FUNCTION
Chapter 3-7
7
Understand Function Notation
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) = 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.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 3-8
8