Functions are defined as a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)
(definition by wordnetweb.princeton.edu/perl/webwn)
In other words, for every "y" value, there is a unique "x" value, such that a "x" value does NOT have more than ONE "y" value. This is one of the key defining factors of a function, and can be tested by a method commonly referred to as the vertical line test.
The vertical line test is conducted by drawing a straight line that forms a 90 degree angle with the x-axis through any point on the graph. If the relationship is truly a function, then it will pass the vertical line test at any location on its graph, modeling the relationship in which there is a unique "x" for every "y."
Functions are used to find the out put of an equation when a certain input is plugged in. They are often written in the form - f(x) - in which the entire expression - f(x) - is the "y" value, and the - (x) - is the "x" input.
To find the output, the function will give you an "x" value to plug in by writing it like this: f(3) in which "3" is the "x" value you are substituting
The written form of a function basically says, if THIS value is plugged in for EVERY "x" in the equation, then THAT value will come out.
ex. f(x) = 10x + 5
f(4) = 10(4) + 5
f(4) = 40 + 5
f(4) = 45
This states that for THIS function, and input of "4" as the "x" value gives you an output of "45" as the "y" value. this point on a coordinate place would be plotted as (4, 45).
This will be my first actual concept post on this blog. This is simply a test to see what method I should use in order to tutor people more efficiently. If you have any requests for this post or would like me to make a post on another concept, be sure to drop me a comment and I'll get to work on it as soon as I can, good luck! :)
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