Precalculus

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Precalculus

• Part I Orientation to Functions

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Precalculus

• Part I Orientation to Functions
• Day 1 The Cartesian Plane

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Precalculus

• Part I Orientation to Functions
• Day 1 The Cartesian Plane
• Day 2 Intelliplotting 2005

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Key Skill Plot a given equation.
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Key Skill Plot a given equation.
Preliminary Consideration Is the equation
suitable for the Cartesian plane?
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Key Skill Plot a given equation.
Preliminary Consideration Is the equation
suitable for the Cartesian plane?
Yes, if the number of explicit variables
displayed in the equation is either 1 or 2.
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Examples
Not suitable for the Cartesian plane 2 3 5
? no explicit variables x2 y2 z2
27 ? 3 explicit variables x, y, z
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Examples
Not suitable for the Cartesian plane 2 3 5
? no explicit variables x2 y2 z2
27 ? 3 explicit variables x, y, z Suitable for
the Cartesian plane x 3 y 2x 5 y -2 x2
y2 25
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Example
Consider the equation y 2x 5 Preliminary
Is the equation suitable for the Cartesian plane?
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Example
Consider the equation y 2x 5 Preliminary
Is the equation suitable for the Cartesian
plane? The explicit variables are y and x. There
are two explicit variables. Hence, the equation
is suitable for the Cartesian plane.
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Methods of Graphing
There are two methods of plotting a given
equation
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Methods of Graphing
There are two methods of plotting a given
equation

• Random Point Plotting

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Methods of Graphing
There are two methods of plotting a given
equation

• Random Point Plotting
• and
• Intelliplotting 2005

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Random Point Plotting
Given an equation y 2x 5 and a
point (1,2) Does the point fit the equation?
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Random Point Plotting
Given an equation y 2x 5 and a
point (1,2) Does the point fit the
equation? Answer 2 2(1) 5?
Yes No
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Random Point Plotting
Given an equation y 2x 5 and a
point (1,2) Does the point fit the
equation? Answer 2 2(1) 5?
Yes No
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Random Point Plotting
Given an equation y 2x 5 and a
point (1,2) Does the point fit the
equation? Answer 2 2(1) 5? So, do not plot
the point (1,2).
Yes No
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Random Point Plotting
Given an equation y 2x 5 and a
point (-2,1) Does the point fit the equation?
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Random Point Plotting
Given an equation y 2x 5 and a
point (-2,1) Does the point fit the
equation? Answer 1 2(-2) 5?
Yes No
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Random Point Plotting
Given an equation y 2x 5 and a
point (-2,1) Does the point fit the
equation? Answer 1 2(-2) 5? So, plot the
point (-2,1).
Yes No
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Random Point Plotting
Given an equation y 2x 5 and a
point (-2,1) Does the point fit the
equation? Answer 1 2(-2) 5? So, plot the
point (-2,1) Continue until you have plotted
enough points to get a grip on the graph of the
equation.
Yes No
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However, there is a much better method of
graphing a given equation than random point
plotting. Random plotting is very inefficient.
Most points tested wont fit the equation.
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Intelliplotting 2005
Preliminary put equation into the y format.
y 2x 5 add 2x to both sides y 2x
5
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Intelliplotting 2005
Intelliplotting has two major components
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Intelliplotting 2005
Intelliplotting has two major components

• Mind plotting
• and
• Techno plotting

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Mindplotting y 2x 5
Step 1 Make a table of friendly values.
x -2 -1 0 1 2
y
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Mindplotting y 2x 5
Step 1 Make a table of friendly values.
x -2 -1 0 1 2
y 2(-2 )51 2(-1)53
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Mindplotting y 2x 5
Step 1 Make a table of friendly values.
x -2 -1 0 1 2
y 1 3 5 7 9
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Mindplotting y 2x 5
Step 1 Make a table of friendly values.
Step 2 Plot the points.
x -2 -1 0 1 2
y 1 3 5 7 9
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Mindplotting y 2x 5
Step 1 Make a table of friendly values.
Step 2 Plot the points.
y
x -2 -1 0 1 2
y 1 3 5 7 9
x
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Mindplotting y 2x 5
Step 3 Smoothly join the points.
Step 1 Make a table of friendly values.
Step 2 Plot the points.
y
y
x -2 -1 0 1 2
y 1 3 5 7 9
y 2x5
x
x
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Intercepts
As part of intelliplotting, determine the
intercepts,
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Intercepts
As part of intelliplotting, determine the
intercepts, those points where the graph crosses
the axes.
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Intercepts
As part of intelliplotting, determine the
intercepts, those points where the graph crosses
the axes.
y-intercept graph crosses the y-axis.
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Intercepts
As part of intelliplotting, determine the
intercepts, those points where the graph crosses
the axes.
y-intercept graph crosses the y-axis.
y
Set x 0 and solve for y
y 2x 5 y 2(0) 5 y 5
(0,?)
Hence, the y-intercept is (0,5).
x
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Intercepts
x-intercept graph crosses the x-axis.
y
Set y 0 and solve for x
y 2x 5 0 2x 5 x -5/2
(?,0)
Hence, the x-intercept is (-5/2,0).
x
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Technoplotting
Construct a graph using technology

• Graphing calculator
• or
• Computer

• xplore
• WinPlot

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xplore
gt graph(2x5, x-3 to 3, colorred, rangetrue)
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WinPlot
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For really cool graphs, apply.
Intelliplotting 2005