Difference between revisions of "Proportion"
m (minor) |
(→Inverse proportion) |
||
| Line 18: | Line 18: | ||
:<math>xy=k</math> | :<math>xy=k</math> | ||
| − | where k is some real number that does not equal zero. | + | where '''k''' is some real number that does not equal zero. |
| − | The graph of an inverse proportion is always a [[hyperbola]], with [[asymptote]]s at the x and y axes. | + | The graph of an inverse proportion is always a [[hyperbola]], with [[asymptote]]s at the x and y axes. |
==Exponential proportion== | ==Exponential proportion== | ||
Revision as of 19:26, 14 September 2007
| This is an AoPSWiki Word of the Week for Sep 13-19 |
Two numbers are said to be in proportion to each other if some numeric relationship exists between them. There are several types of proportions, each defined by a separate class of function.
Direct proportion
Direct proportion is a proportion in which one number is a multiple of the other. Direct proportion between two numbers x and y can be expressed as:
where k is some real number.
The graph of a direct proportion is always linear.
Often, this will be written as 
.
Inverse proportion
Inverse proportion is a proportion in which as one number's absolute value increases, the other's decreases in a directly proportional amount. It can be expressed as:
where k is some real number that does not equal zero.
The graph of an inverse proportion is always a hyperbola, with asymptotes at the x and y axes.
Exponential proportion
A proportion in which one number is equal to a constant raised to the power of the other, or the logarithm of the other, is called an exponential proportion. It can be expressed as either:
or
or
for some real number k, where k is not zero or one.
