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
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