Functions: Even/Odd/Neither

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# Functions: Even/Odd/Neither - PowerPoint PPT Presentation

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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### 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 &

x-axis (or symmetrical about the origin),

then it’s odd. **Fold hotdog & hamburger!

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.

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

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.

Examples: Graphically

Neither

Even

Odd

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