Graphs

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Section 3.1
Graphs
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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DEFINITION
Standard Form of Linear Equations

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PROCEDURE
Finding the Intercepts

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RULE
Graphing Horizontal and Vertical Lines
Y C is a horizontal line.
X C is a vertical line.
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Practice TestExercise 1
Chapter 3 Graphs and FunctionsSection 3.1A
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b. Find the coordinates of the points in the
figure.
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Practice TestExercise 2
Chapter 3 Graphs and FunctionsSection 3.1A
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Graph the solutions to
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Graph the solutions to
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Practice TestExercise 3
Chapter 3 Graphs and FunctionsSection 3.1C
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Find the x- and y- intercepts of y 3x 2 and
then graph the solutions to the equation.
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Find the x- and y- intercepts of y 3x 2 and
then graph the solutions to the equation.
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Find the x- and y- intercepts of y 3x 2 and
then graph the solutions to the equation.
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Practice TestExercise 4
Chapter 3 Graphs and FunctionsSection 3.1D
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Graph the solutions to
a.
b.
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Section 3.2
Introduction to Functions
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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DEFINITION

Relation, Domain, and Range
Relation A set of ordered pairs.
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DEFINITION

Relation, Domain, and Range
Domain A set of first coordinates.
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DEFINITION

Relation, Domain, and Range
Range A set of second coordinates.
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DEFINITION

Function
A relation in which no two different ordered
pairs have the same first coordinates.
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PROCEDURE

Vertical Line Test
If a vertical line intersects the graph more than
once, the relation is not a function.
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DEFINITION

Linear Function
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DEFINITION

Function

• A function assigns exactly one range value to
  each domain value.

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DEFINITION

Function
2. A function is a relation in which no two
ordered pairs have the same first coordinate.
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DEFINITION

Function
3. A function assigns one range to each domain.
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Practice TestExercise 5
Chapter 3 Graphs and FunctionsSection 3.2A
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Find the domain and range of the relation (1,
3), (2, 5), (3, 7), (4, 9).
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Practice TestExercise 7c
Chapter 3 Graphs and FunctionsSection 3.2A
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Find the domain and range of the relation.
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Practice TestExercise 8b
Chapter 3 Graphs and FunctionsSection 3.2B
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Use the vertical line test to determine whether
the graph of the given relation defines a
function.
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Practice TestExercise 9
Chapter 3 Graphs and FunctionsSection 3.2C
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Find the domain of the function.
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Practice TestExercise 10
Chapter 3 Graphs and FunctionsSections 3.2D
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Let (x) 4x 3. Find
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Let (x) 4x 3. Find
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Let (x) 4x 3. Find
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Practice TestExercise 11c
Chapter 3 Graphs and FunctionsSection 3.2D
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Let (1, 4), (2, -1), (3, 2). Find
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Section 3.3
Using Slopes to Graph Lines
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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DEFINITION

Slope
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RULES

Slopes of Parallel Lines
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RULES

Slopes of Perpendicular Lines
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DEFINITION

The Slope-Intercept Form of a Line
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Practice TestExercise 13b
Chapter 3 Graphs and FunctionsSection 3.3B
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AB is neither parallel nor perpendicular.
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Practice TestExercise 14
Chapter 3 Graphs and FunctionsSection 3.3B
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Practice TestExercise 15
Chapter 3 Graphs and FunctionsSection 3.3C
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Practice TestExercise 16
Chapter 3 Graphs and FunctionsSection 3.3D
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Section 3.4
Equations of Lines
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OBJECTIVES
Find the equation and graph of a line given
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OBJECTIVES
Find the equation and graph of a line given
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OBJECTIVES
Find the equation and graph of a line given
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OBJECTIVES
Find the equation and graph of a line given
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OBJECTIVES
Find the equation and graph of a line given
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OBJECTIVES
Find the equation and graph of a line given
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OBJECTIVES
Find the equation and graph of a line given
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Point-Slope Form of a Line

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DEFINITION
The Slope-Intercept Form of a Line

slope
y-intercept
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Practice TestExercise 17
Chapter 3 Graphs and FunctionsSection 3.4A
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Find an equation of the line through (4, 3) and
(2, 4). Then write the equation in standard form
and graph the line.
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Find an equation of the line through (4, 3) and
(2, 4). Then write the equation in standard form
and graph the line.
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Find an equation of the line through (4, 3) and
(2, 4). Then write the equation in standard form
and graph the line.
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Practice TestExercise 18
Chapter 3 Graphs and FunctionsSections 3.4B
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Find an equation of the line with slope 2 and
passing through the point (2, 3). Then graph the
line.
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Find an equation of the line with slope 2 and
passing through the point (2, 3). Then graph the
line.
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Practice TestExercise 19
Chapter 3 Graphs and FunctionsSection 3.4C
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A line has slope 3 and y-intercept 2. Find the
slope-intercept equation of this line and graph
the line.
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A line has slope 3 and y-intercept 2. Find the
slope-intercept equation of this line and graph
the line.
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Practice TestExercise 20
Chapter 3 Graphs and FunctionsSection 3.4D
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Find an equation of the line through the point
(1,2) and
a.
Parallel to the line 2x 3y 5. Write in
standard form.
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Find an equation of the line through the point
(1,2) and
a.
Parallel to the line 2x 3y 5. Write in
standard form.
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Find an equation of the line through the point
(1,2) and
negative reciprocal
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Practice TestExercise 22
Chapter 3 Graphs and FunctionsSection 3.4E
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Given that a line passes through the point ( 2,
4), find the equation of the line if it is a
vertical line.
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Practice TestExercise 23
Chapter 3 Graphs and FunctionsSection 3.4F
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The points in the table represent a linear model.
Plot the points on a graph, draw the line of best
fit, and write the equation of that line in
slope-intercept form.
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Graph.
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Section 3.5
Linear Inequalities in Two Variables
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OBJECTIVES
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OBJECTIVES
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DEFINITION
Linear Inequality In Two Variables

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PROCEDURE
Graphing a Linear Inequality

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PROCEDURE
Graphing a Linear Inequality

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PROCEDURE
Graphing a Linear Inequality

3. If the test point satisfies the inequality,
shade the region containing the test point.
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PROCEDURE
Graphing a Linear Inequality

3. Otherwise, shade the region on the other side
of the line. The shaded region represents all
solutions.
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Practice TestExercise 24
Chapter 3 Graphs and FunctionsSection 3.5A
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Graph.
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Graph.
Related boundary y 1
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Practice TestExercise 25a
Chapter 3 Graphs and FunctionsSection 3.5B
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Graph.
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AdditionalExercises
Chapter 3 Graphs and Functions