Symmetry and Coordinate Graphs Section 3-1

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3.1 Symmetry & Coordinate Graphs

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Presentation transcript:

Symmetry and Coordinate Graphs Section 3-1 Essential Questions: How do we determine symmetry using algebra? How do we classify functions as even or odd?

Possible types of symmetry are: with respect to the x-axis with respect to the y-axis with respect to the origin with respect to the line y = x with respect to the line y = -x

Table of Symmetric Relationships Symmetry with respect to: What do we do? Example x-axis y-axis origin y = x y = -x

Equals original function x-axis What we do: keep x the same but negate y (1, 2) (1, -2) Equals original function

Equals original function y-axis What we do: keep y the same but negate x (-1, 2) (1, 2) Equals original function

Equals original function What we do: negate x AND negate y (-1, 3) (1, -3) Equals original function

Equals original function y = x What we do: interchange (swap) x and y (2, 3) (3, 2) Equals original function

Equals original function y = -x What we do: interchange AND negate x and y (2, 3) (-3, -2) Equals original function

Example 1 x-axis y-axis origin y = x y = -x No Yes Determine the types of symmetry for the graph of xy = -2 x-axis y-axis origin y = x y = -x No Yes

Example 2 x-axis yes y-axis origin y = x no y = -x Determine the types of symmetry for the graph of x-axis y-axis origin y = x y = -x yes no

Classifying Functions as Even or Odd EVEN functions are symmetric with respect to the y-axis ODD functions are symmetric with respect to the origin