Every function can be classified as an even function, an odd function, or neither. Even functions have the characteristic that f (x) = f (-x). They are symmetrical with respect to the y-axis. A line segment joining the points f (x) and f (-x) will be perfectly horizontal , shown by dotted blue line in the applet below.

Odd functions have the characteristic that f (x) = - f (-x). They are symmetrical with respect to the origin. A line segment joining the points f (x) and f (-x) always contains the origin , shown by dotted red line in the applet below.

Some of the most common even functions are y = k , where k is a constant, y= x

Formal tests for symmetry:

1. y – axis : replace x with –x , produces an equivalent equation

2. x - axis : replace y with – y , produces an equivalent equation

3. origin : replace x with –x and y with –y , produces equivalent equation.

In the following applet use

Odd functions have the characteristic that f (x) = - f (-x). They are symmetrical with respect to the origin. A line segment joining the points f (x) and f (-x) always contains the origin , shown by dotted red line in the applet below.

Some of the most common even functions are y = k , where k is a constant, y= x

^{2}, and y = cos(x) . Some of the most common odd functions are y = x^{3}and y = sin(x) . Some functions that are neither even nor odd include y = x - 4 , y = cos(x) + 1.Formal tests for symmetry:

1. y – axis : replace x with –x , produces an equivalent equation

2. x - axis : replace y with – y , produces an equivalent equation

3. origin : replace x with –x and y with –y , produces equivalent equation.

In the following applet use

**check box**to select between odd or even functions. Also you can enter any function in the input box to see whether it is odd or even by checking the symmetry about y-axis or origin.
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