Graphs and Graphing Utilities

1. Section 1.1 Graphs and Graphing Utilities

2. Points and Ordered Pairs

3. 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)

4. Example Plot the following points: (-4,3), (-1,-1), (0,3), (2,-4), (3,0)

5. Graphs of Equations

6. The graph of an equation in two variables is the set of all points whose coordinates satisfy the equation. 1 2 -2 1 -3 0 -2 -1 1 -2 y x

7. Example Graph the following equation and construct a table: y x

8. Graphing Equations and Creating Tables Using a Graphing Utility

9. Graphing Calculators or graphing software packages for computers are referred to as graphing utilities or graphers. Below you will find the viewing rectangle.

10. Graphing Calculator The 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.

11. Graphing Calculator Making a Table Press 2 nd 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 X 2 then and finally 9

12. Example Given the following viewing window, put the numbers on the screen. [-50,50,10] by[-40,40,10]

13. Intercepts

14. The x and y intercepts can be seen on a graphing calculator Y intercept

15. For the x intercept, the y-coordinate is 0. ( ,0) For the y intercept, the x-coordinate is 0. ( 0, ) What are the x and y intercepts? 0 0 y x

16. Example Find the x and y intercepts and graph the equation after plotting a few more points. 0 0 y x

17. Interpreting Information Given by Graphs

19. (a) (b) (c) (d) Find the x and y intercepts for the equation ?