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