Download 1.1_Graphs and Graphing Utilities short

We are starting
actual
Precalculus
today!!!
• Please pick up a notes sheet from the red bin
• Please pick up a textbook from the open closet (to the
left)
• A Text book sign out sheet will be passed around for you
to complete (Book Number, Signature). You cannot
leave class today without doing that! Side note, there
might not be enough books for everyone. I promise to
get you a book by Monday :-/
• Calculators will also be assigned today!
SECTION 1.1
GRAPHS AND GRAPHING UTILITIES
POINTS & ORDERED PAIRS
• 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).
Plot the following points:
Example
(-4,3), (-1,-1), (0,3), (2,-4), (3,0)
y




x













GRAPHS OF EQUATIONS
• The graph of an equation in two variables is the set of all
points whose coordinates satisfy the equation.
• You can always create a table (or T-chart) in order to graph.
y  x 3
y
2




x













x
-2
-1
0
1
2
y
1
-2
-3
-2
1
Example
Graph the following equation and construct a table:
y  x2
x
y
Graphing Equations and Creating Tables
Using a Graphing Utility
Graphing
Calculators or
graphing software
packages for
computers are
referred to as
graphing utilities
or graphers.
Press the home screen key.
Select 1: New Doc. We are going to make a
graph (option 2).
Now type in the equation x2 - 2 & Enter.
GRAPHING CALCULATOR
THE VIEWING SCREEN
Ymax
•The Xscl and Yscl are the
spacing between tick marks.
•Press Menu (to the right of
the click pad) you can
change the settings by
picking 4: Window/Zoom.
Choose 1: Window Settings.
Xscl
Xmax
Xmin
•We express this window’s dimensions as
[-8,8,1] by [-4,10,1]. X dimensions are first
and Y dimensions second. Use tab to get
from field to field.
•Now change your window to [-10,10,1] by
[-10,10,1]. To get back to the standard
setting press Menu, 4:Window/Zoom, then
option 5:Zoom - Standard.
Yscl
Ymin
Example
Given the following viewing window, put the numbers on
the window below.
[-50,50,10] by[-40,40,10]
y
x
GRAPHING CALCULATOR
MAKING A TABLE
We are going to
make another graph.
Hit ctrl and doc to
insert the new page.
Now type in the equation
x2/ 9 and Enter.
Press Ctrl T. What
happens?
Press Ctrl T again.
What happens?
Intercepts
X-intercept (1, 0)
X-intercept (-4, 0)
Y intercept, (0, -4)
[-10, 10, 1] by [-6.67, 6.67, 1]
The x and y intercepts can be seen on a graphing
calculator.
For the x intercept, the y-coordinate is 0.
(
,0)
For the y intercept, the x-coordinate is 0.
( 0,
)
y
y  x 4
2




x
y
??
0
0
??
x













What are the x and
y intercepts?
Find the x and y intercepts
and graph the equation after
plotting a few more points.
Example
y  x2
y




x
y
??
-2
0
0
??
2
x













No x and 1 y
1x and No y
y
y








x








x



















1 x and 3 y
No x and No y
y
y








x









x
















Same x and Same y
y




x













Interpreting Information Given by Graphs
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?
Exit Ticket
Find the x and y intercepts for the
2
equation y   x  9 ?
(a)  3,0  3,0  9,0 
(b)  3,0  3,0  0,9 
(c)  0,0  0, 3  0,9 
(d)  3,0  3,0  3,0 
(b)
Graph the following equation
by letting x=-2,-1,0,1,2.
1
y   x 1
2
x y
-2
-1
0
1
2
y
y


(a)
(b)






x
x



















(a)



(c)




(d)
y

y







x








x

















