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Functions: Even/Odd/Neither

Functions: Even/Odd/Neither. Math I: Unit 5 (Part 2). Graphically…. A function is even… . If the graph is symmetrical about the y-axis, then it’s even. **Fold hotdog!. Graphically…. A function is odd…. If the graph is symmetrical about the y-axis &

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Functions: Even/Odd/Neither

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  1. Functions: Even/Odd/Neither Math I: Unit 5 (Part 2)

  2. Graphically… • A function is even… If the graph is symmetrical about the y-axis, then it’s even. **Fold hotdog!

  3. Graphically… • A function is odd… If the graph is symmetrical about the y-axis & x-axis (or symmetrical about the origin), then it’s odd. **Fold hotdog & hamburger!

  4. Algebraically… • A function is even if f(-x) = f(x) Example 1: f(x) = 2x2 + 5 If you substitute in -x and get the SAME function that you started with, then it’s even. The equations are exactly the SAME…so EVEN function.

  5. Algebraically… • A function is odd if f(-x) = -f(x) If you substitute in -x and get the OPPOSITE function (all the signs change),then it’s odd. Example: f(x) = 4x3 + 2x EVERY sign changed…so OPPOSITES… ODD function

  6. Neither… • Graphically… If a function does not have y-axis symmetry OR origin symmetry…then it has NEITHER. • Algebraically… If, after substituting –x in place of x, the equation is not EXACTLY the same OR complete OPPOSITES, then the function is NEITHER.

  7. Examples: Graphically Neither Even Odd

  8. Examples: Algebraically f(x) = x4 + x2 f(x) = 1 + x3 f(x) = 2x3 + x SAME – so EVEN Not same and Not all signs changed – so NEITHER OPPOSITES– so ODD

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