2.2 Graphs of Equations

Symmetric to X – Axis For every point (x, y) on the graph,

the point (x, y) is also on the graph.

Symmetric to Y – Axis For every point (x, y) on the graph,

the point ( x, y) is also on the graph.

Symmetric to Origin For every point (x, y) on the graph,

the point ( x, y) is also on the graph.

Given a point, find points that are symmetric with

respect to the x-axis, the y-axis, and the origin. 1. 4, 2

3. 0,8 4. 4,6

2. 7, 9

Testing An Equation for SymmetryReplace y by – y in the equation. If an

equivalent equation results, the graph of the equation is symmetric with respect to

the x-axis.Replace x by – x in the equation. If an

equivalent equation results, the graph of the equation is symmetric with respect to

the y-axis.Replace x by – x and y by – y in the

equation. If an equivalent equation results, the graph of the equation is symmetric with

respect to the origin.

Test each equation for symmetry with respect to the x-axis, the y-

axis, and the origin.2 21. 16x 9y 49

23. x 2y 1

22. y x 4

3.1 Functions

A relation is a set of ordered pairs. Relation : {(–2, 6), (4, 2), (3, –4), (0, –2)}

The domain is the set of all the first coordinates of the ordered pairs. Domain : {–2, 4, 3, 0}

The range is the set of all the second coordinates of the ordered pairs. Range : {6, 2, –4, –2}

A function is a relation in which each element in the domain is paired with one

and only one element in the range.

T 7,1, 4,3 , 7,6 Not Function

R 5,2 , 4,6 , 2,7 , 3,2 Function

S 2,1, 4,2 , 6,3 , 8,4 Function

Domain of A Function

3. y 5x 4

44. y

3x 2

D ,

3 3D , ,

4 4

4D ,

5

2D ,

3

2x2. y

4x 3

1. y 4x 5

For each of the following relations, state the domain and range. Also, indicate if

the relation is a function. 1. M 4,1, 2,8 , 3,6 , 6,1

2. y x 2 6

3. y 4 x 2 5

24. x 2y 7