4.3 Symmetry Which graph is NOT a function?

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Presentation transcript:

4.3 Symmetry Which graph is NOT a function? Re-write the graph as two separate functions. Now match each graph with its description. Absolute Value Cubic Square Root Parabola Constant Linear

Reflection over x-axis Reflection over y-axis

Reflection over line y = x

Symmetry

Checking for Symmetry: algebraically then graphically

Checking for Symmetry: algebraically then graphically Checking for Symmetry: algebraically only

Completing the Graph Symmetric with respect to the origin Symmetric with respect to the y-axis Symmetric with respect to the origin Symmetric with respect to the origin Symmetric with respect to the x-axis

Point of Symmetry Homework All “odd” functions have a point of symmetry: where it is possible to pair the points of the graph in such a way that the point of symmetry is the midpoint of the segment joining each pair. Homework Pages 136–138 #1, 47, 9, 12, 14, 15 (a, b), 21a, 23a, 31 (a, b, c), 35, 36

Absolute Value Unchanged when f(x) ≥ 0 and reflected in the x-axis when f(x) < 0.