1. P.1 Graphs and Models

2. Objectives Sketch the graph of an equation.
Find the intercepts of a graph.
Test a graph for symmetry with respect to an axis and the origin.
Find the points of intersections of two graphs.
Interpret mathematical models for real-life data.

3. Graphing
One way to sketch a graph is to plot points as in example 1 on page 2.
You can get an inaccurate graph if you plot too few points.

4. Graphing Calculator Zoom feature Window settings
Zoom 6 (non-trig functions)
Zoom 7 (trig functions)
Window settings

5. Intercepts x-intercepts: where the graph crosses the x-axis (y=0)
y-intercepts: where the graph crosses the y-axis (x=0)
Calculator
Calculate Value x=0
Calculate Zero

6. Example
Find x- and y-intercepts of the graph of

7. Symmetry y-axis (x, y) (-x, y) x-axis (x, y) (x, -y) origin

8. Test for Symmetry Replace x by –x  y-axis Replace y by –y  x-axis
Replace x by –x and y by –y  origin

9. Shortcut IF POLYNOMIALS
All even powers of x  y-axis
All odd powers of x  origin
All even powers of y  x-axis

10. Example

11. Other examples
y-axis
origin
neither

12. Example We can use symmetry to help sketch a graph.
is symmetric to the x-axis.
all even powers of y, or
can replace y by –y
Can sketch upper part of graph by plotting points then reflect across the x-axis.

13. Graphing Calculator How do you graph this on the calculator?
To graph on the calculator, you have to solve for y and then plot BOTH equations.

14. Points of Intersection
To find points of intersection you "solve a system of equations".
substitution
elimination

15. Example
Find all points of intersection of the graphs of

16. Homework P.1: page 8 #1-4 all 19-41 odd 51-57 odd 63-69 odd
(Don't sketch 41-57)