Transcript Chapter 3-7

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
§ 3.7
Graphing Linear
Inequalities
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 3-3
3
Graph Linear Inequalities
Linear Inequality in Two Variables
A linear inequality in two variables can be written in one of the
following forms:
ax + by < c, ax + by > c, ax + by ≤ c, ax + by ≥ c
where a, b, and c are real numbers and a and b are not both 0.
Examples:
2x + 3y > 2
-x – 2y ≤ 3
3y < 4x - 9
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 3-4
4
Graph Linear Inequalities
Consider the graph of the equation x + y = 3. The line
acts as a boundary between two half-planes and
divides the plane into three distinct sets of points.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 3-5
5
Graph Linear Inequalities
1.
2.
3.
To get the equation of the boundary line, replace the
inequality symbol with an equals sign.
Draw the graph of the equation in step 1. If the original
inequality contains a  or  symbol, draw the boundary
line using a solid line. If the original inequality contains
a < or > symbol, draw the boundary line using a dashed
line.
Select any point not on the boundary line and determine
if this point is a solution to the original inequality. If the
point selected is a solution, shade the half-plane on the
side of the line containing this point. If the selected
point does not satisfy the inequality, shade the halfplane on the side of the line not containing the point.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 3-6
6
Graph Linear Inequalities
Graph y < 2x + 1.
dashed line
Checkpoint (0, 0 )
satisfies the
inequality.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 3-7
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