Section 1.1 Graphs and Graphing Utilities

Points and 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)

Example Plot the following points:

(-4,3), (-1,-1), (0,3), (2,-4), (3,0)

x

y

Graphs of Equations

The graph of an equation in two variables is the set of all points whose coordinates satisfy the equation.

2 3y x

x y

-2 1

-1 -2

0 -3

1 -2

2 1

x

y

Example

Graph the following equation and construct a table: 2y x

x

y

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. Below you will find the viewing rectangle.

Graphing CalculatorThe Viewing Rectangle

Xmin Xmax

Ymax

Ymin

Xscl

Yscl

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.

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.

Graphing CalculatorMaking a Table

Press 2nd Window in order to Set up the Table.

Press 2nd Graph to see the Table of values.

Press the blue key in the upper left corner that says y= Now type in the equation. X,T,,,,n then X2 then

and finally 9

Example

Given the following viewing window, put the numbers on the screen.

[-50,50,10] by[-40,40,10]

x

y

Intercepts

The x and y intercepts can be seen on a graphing calculator

Y intercept

For the x intercept, the y-coordinate is 0. ( ,0)

For the y intercept, the x-coordinate is 0. ( 0, )

x

y

2 4y x x y

0

0

What are the x and y intercepts?

Example Find the x and y intercepts and graph the equation after plotting a few more points.

x

y

2y x

x y

0

0

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?

(a)

(b)

(c)

(d)

Find the x and y intercepts for the equation ?

2 9y x

3,0 3,0 9,0

3,0 3,0 0,9

0,0 0, 3 0,9

3,0 3,0 3,0

(a) (b)

(c) (d)

Graph the following equation by letting x=-2,-1,0,1,2.

11

2y x

x y

-2

-1

0

1

2

x

y

x

y

x

y

x

y