Download Chapter 3-1

Chapter 3
Graphs and
Functions
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 3-1
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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
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§ 3.1
Graphs
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 3-3
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Definitions
A graph shows the relationship between two
variables in an equation.
The Cartesian (rectangular) coordinate system is
a grid system used to draw graphs. It is named
after its developer, René Descartes (1596-1650).
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Chapter 3-4
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Definitions
y
II
I
x
III
IV
The two intersecting axis form four quadrants,
numbered I through IV.
The horizontal axis is called the x-axis.
The vertical axis is called the y-axis.
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Chapter 3-5
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Definitions
y
Origin
x
(0, 0)
The point of intersection of the two axes is called
the origin.
The coordinates, or the value of the x and the
value of the y determines the point. This is also
called an ordered pair.
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Chapter 3-6
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Plotting Points
Starting at the
origin, move 3
places to the right.
Plot the point (3, -4).
The x-coordinate is 3 and the y-coordinate is –4.
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Chapter 3-7
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Plotting Points
Then move
4 places
down.
Plot the point (3, -4).
The x-coordinate is 3 and the y-coordinate is –4.
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Chapter 3-8
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Plotting Points
(3, -4)
Plot the point (3, -4).
The x-coordinate is 3 and the y-coordinate is –4.
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Chapter 3-9
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Linear Equations
A linear equation in two variables is an
equation that can be put in the form
ax + by = c
where a, b, and c are real numbers.
This is called the standard form of an equation.
Examples:
4x – 3y = 12
x + 2y = -35
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Chapter 3-10
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Solutions to Equations
The solution to an equation is the ordered pair
that can be substituted into the equation
without changing the “validity” of the
equation.
Is (3, 0) a solution to the equation 4x – 3y = 12?
4x – 3y = 12
4(3) – 3(0) = 12
12 – 0 = 12
12 = 12  Yes, it is a solution.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 3-11
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Graphing
A graph of an equation is an illustration of the set
of points whose ordered pairs are solutions to
the equation.
A set of points that are in a straight line are
collinear.
The points
(-1, 4), (1, 1) and (4, -3)
are collinear.
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Chapter 3-12
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Graph Nonlinear Equations
Equations whose graphs are not straight lines are
called nonlinear equations.
Example: Graph y = x2 – 4. Use the following values for
x: -3, -2, -1, 0, 1, 2, and 3.
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Chapter 3-13
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