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This unit covers the concept of symmetry in graphs, specifically how points can be symmetric with respect to the x-axis, y-axis, and origin. Symmetry tests are explained with practical methods to determine if a graph maintains its mirror image across these axes. For the x-axis, we check the equation by replacing y with -y; for the y-axis, we replace x with -x; and for the origin, we replace both x and y with their negatives. Homework exercises reinforce these concepts through practical application.
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Unit 1 Graphs Symmetry
Symmetric Points • Symmetric with respect to the x-axis: (x, y) → (x, -y) • Symmetric with respect to the y-axis: • (x, y) → (-x, y) • Symmetric with respect to the origin: • (x, y) → (-x, -y)
Tests for symmetry on graphs • X-axis: • Replace y by –y in the equation. If an equivalent equation results, the graph is symmetric with respect to the x-axis. • Y-axis: • replace x by –x in the equation. If an equivalent equation results, then the graph is symmetric with respect to the y-axis. • Origin: • replace x by –x and y by –y in the equation. If an equivalent equation results, then the graph is symmetric with respect to the origin.
Homework: • p. 30-31 (1-9 odd, 11-22 all, 23-27 odd)
