2.2 Graphs of Equations.

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Presentation transcript:

2.2 Graphs of Equations

Symmetric to X – Axis

Symmetric to Y – Axis

Symmetric to Origin

Given a point, find points that are symmetric with respect to the x-axis, the y-axis, and the origin.

Testing An Equation for Symmetry Replace 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.

3.1 Functions

A relation is a set of ordered pairs 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.

Domain of A Function

For each of the following relations, state the domain and range For each of the following relations, state the domain and range. Also, indicate if the relation is a function.