Section P.1 – Graphs and Models

How to Graphx yMake a table to graph y = x2 + 2

-5

-4

-3

-2

-1

0

1

2

3

4

5

Use your knowledge of relations and functions to make sure you pick

values of x that make a

complete graph.

27

18

11

6

3

2

3

6

11

18

27You do not need to plot every point, but make sure

to get the complete graph.

Only use a ruler if the relation is linear.

Definitions

x-intercept Where the graph crosses the x-axis OR The value of x when y is 0.

y-intercept Where the graph crosses the y-axis OR The value of y when x is 0.

Types of SymmetryWith Respect to the…

y-axis x-axis origin

Tests…

Replacing x in the equation by –x yields

an equivalent equation.

Replacing y in the equation by –y yields

an equivalent equation.

Replacing x in the equation by –x and y

by –y yields an equivalent equation.

Example of SymmetryTest for symmetry in the equation .4y x

4y x

4y x

Check out the graph first. Test by Replacing x in the equation by –x.

The equation is symmetric with respect to the y-axis.

An equivalent equation.

System of Equations Example

Solve the following system of equation algebraically:

2 22

3 28

y x

y x

22 3 822 xx 22 5 28x

50 5x10 x

3 10 28y 30 28y 2y

10,2

y

2 22x Both equations equal y. Set them

equal to each other.

System of Equations Example

2 2 18

3

x y

x y

Solve the following system of equation algebraically:

2 2 83 1y y 6 2 2 18y y

6 18

No Solution.

3 yx

FALSE

The two lines are parallel. They

never intersect.

System of Equations Example

Solve the following system of equation algebraically:

2 22

3 28

y x

y x

22 3 822 xx 22 5 28x

50 5x10 x

3 10 28y 30 28y 2y

10,2

y

2 22x