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 3-2

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

Chapter Sections

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

§ 3.3

Linear Functions: Graphs and Applications

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

Graph Linear Functions

Linear Function

A linear function is a function of the form f(x) = ax + b

• The graph of any linear equation is a straight line.• The domain of any linear function is all real numbers.• If a ≠ 0, then the range of any linear function is all real numbers.

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-5

Graph Linear Functions Using Intercepts

Standard Form of Linear Equation

The standard form of a linear equation is

ax + by = c

where a, b, and c are real numbers, and a and b are not both 0.

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

Graph Linear Functions Using Intercepts

x- and y-intercepts

The x-intercept is the point at which a graph crosses the x-axis.

• The x- intercept will always be of the form (x,

0).The y-intercept is the point at which a graph crosses the y-axis.

• The y-intercept will always be of the form (0,

y).

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-7

Graph Linear Functions Using Intercepts

To Graph Linear Equations Using the x- and y-intercepts

1. Find the y-intercept. Set x equal to 0 and find the corresponding value for y.

2. Find the x-intercept. Set y equal to 0 and find the corresponding value for x.

3. Plot the intercepts.4. Draw the line. Using a straightedge, draw

a line through the points. Draw an arrowhead at both ends of the line.

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-8

Graph Using Intercepts

This gives us the y-intercept (0, 2).

Example: Graph 5x = 10y – 20 using the x- and y-intercepts.

Solution To find the y-intercept, set x = 0 and solve for y.

y

y

y

y

yx

2

1020

20100

2010)0(5

20105

9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-9

Graph Using Intercepts

This gives us the x-intercept (-4, 0).

Use the intercepts (0, 2) and (-4, 0) to graph the linear function.

To find the x-intercept, set y = 0 and solve for x.

4

205

20)0(105

20105

x

x

x

yx

10 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-10

Graph Using Intercepts

Plot the points and draw the line.

11 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-11

Graph Equations of the Form x = a and y = b

Equations of a Horizontal Line

The graph of any equation of the form y = b will always be a horizontal line for any real number b.

Equations of a Vertical Line

The graph of any equation of the form x = a will always be a vertical line for any real number a.