P.1 Graphs and Models

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.

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.

Graphing Calculator

3 2 25y x x

Zoom feature Zoom 6 (non-trig functions) Zoom 7 (trig functions)

Window settings

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

Example

Find x- and y-intercepts of the graph of

3 4 .y x x

y-axis (x, y) (-x, y)

x-axis (x, y) (x, -y)

origin (x, y) (-x, -y)

Symmetry

Test for Symmetry

Replace x by –x y-axis Replace y by –y x-axis Replace x by –x and y by –y origin

Shortcut IF POLYNOMIALS

All even powers of x y-axis All odd powers of x origin

All even powers of y x-axis

Example53 2y x x

Other examples6 22 3 4y x x 5 32 3y x x 5 32 3 1y x x

y-axis

origin

neither

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.

2 1x y

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.

2 1x y

Points of Intersection

To find points of intersection you "solve a system of equations". substitution eliminiation

Example

Find all points of intersection of the graphs of 2 3 and 1.x y x y

Homework

P.1: page 8#1-4 all5-11 odd

17-37 odd47-55 odd63-71 odd

(Don't sketch 37-53)