Tuesday, November 3, 2009

Even and Odd Functions

By definition, an even function is a function that is symmetrical about the y-axis and an odd function is a function that is symmetrical about the origin.

Mathematically, however, the definition looks more like this:

A function y = f(x) is an
even function of x if f(-x) = f(x),
odd function of x if f(-x) = -f(x),
for every x in the function's domain.

Explain how this mathematical definition results in the exact same thing as the first definition. You may use examples to help support your written explanation.




Some vocabulary words that may be useful in this explanation:
  • quadrant (1, 2, 3, and 4)
  • input
  • output
  • opposite (-1 and 1, 3/2 and -3/2, etc.)

2 comments:

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  2. example:

    A function y = f(x) is an
    even function of x if f(-x) = f(x),
    odd function of x if f(-x) = -f(x),
    for every x in the function's domain.

    ...

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