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Section 1.1
Graphs and Graphing Utilities
Plot points on the rectangular coordinate system. Plot the
x coordinate first then the y coordinate. This is an ordered
pair of real numbers. (x,y)
The graph of an equation in two variables is
the set of all points whose coordinates
satisfy the equation.
y
y = x2 − 3
4
3
2
1
x
−4
−3
−2
−1
1
−1
−2
−3
2
3
4
5
x
-2
-1
0
1
2
y
1
-2
-3
-2
1
−4
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Example
Graph the following equation and construct a
table: y = x − 2
y
x
4
y
3
2
1
x
−4
−3
−2
−1
1
2
3
4
5
−1
−2
−3
−4
Graphing Calculators or graphing software
packages for computers are referred to as
graphing utilities or graphers. Below you
will find the viewing rectangle.
Graphing Calculator
The Viewing Rectangle
The meaning of the terms
is demonstrated at right.
This is the window that you
get with the dimensions
chosen by pressing
Window in the top row of
keys on your calculator.
Ymax
Xscl
Xmax
Xmin
Yscl
Ymin
The Xscl and Yscl are the
spacing between tick marks.
We express this window’s dimensions as
[-8,8,1] by [-4,10,1]. X dimensions are first
and Y dimensions second.
To get the standard window
[-10,10,1] x [-10,10,1] press
Zoom, then the number 6,
for Zoom Standard.
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Graphing Calculator
Making a Table
Press the blue key in
the upper left corner
that says y=
Now
type in the equation.
θ then X2 then
X,T,,,,n
÷and finally 9
Press 2nd Window in
order to Set up the
Table.
Press 2nd Graph to
see the Table of
values.
Example
Given the following viewing window, put
the numbers on the screen.
[-50,50,10] by[-40,40,10]
x
Y intercept
The x and y intercepts can be
seen on a graphing calculator
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For the x intercept, the y-coordinate is 0.
(
For the y intercept, the x-coordinate is 0.
( 0,
,0)
)
y
y = x2 − 4
4
3
x y
2
0
1
x
−4
−3
−2
−1
1
2
3
4
5
0
−1
−2
−3
What are the x and
y intercepts?
−4
Find the x and y intercepts
and graph the equation after
plotting a few more points.
Example
y
y = x+2
4
3
x y
2
0
1
x
−4
−3
−2
−1
1
2
3
4
5
0
−1
−2
−3
−4
1. What is the desirable heart rate of a 20 year old
woman during exercise?
2. What is the desirable heart rate of a 20 year old
man during exercise?
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