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You have worked with functions in your previous course. Let's refresh those skills.
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A function is a set of ordered pairs in which each x-element has only ONE y-element associated with it.
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A function is a relationship between variables.
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A function is like a factory machine that has input and output.
The input is the x-value
(called the "domain"),
and the output is the y-value
(called the "range")
of the function.
Each value "enters" the function only once, and has only "one value coming out" of the function.
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While a function may NOT have two y-values assigned to the same x-value,
it may have
two x-values assigned to the same y-value.
NOT OK for a function:
{(5,1),(5,4)} |
OK for a function:
{(5,2),(4,2)} |
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 Vertical Line Test for functions: Any vertical line intersects the graph of a function in only ONE point. |
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Function:
{(1,1),(3,3),(4,4),(5,5),(6,4)} 
Any vertical line will intersect only one point at a time.
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Function: y = x
Any vertical line will intersect the graphed line only once,
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Which of the following graphs represents a function?
Solution: Choice b is the answer. A vertical line drawn on this graph will intersect the graph in only one location, making it a function. Vertical lines on the other three graphs will intersect the graph in more than one location, or as in part a, will intersect in an infinite number of points (all points).
Function notation is the lettering style that is used to represent a function. When dealing with graphing, the "y" value in the equation will be replaced with a different letter followed by a parentheses containing "x".
For example, y = 3x + 2 would be written as f(x) = 3x + 2.
This form of notation is a more precise way of giving information about the function without a rather lengthy written explanation.
For example: If two lines appear on the same coordinate grid, f(x) = 3x + 2 can clearly represent one of the lines and g(x) = 4x - 6 can clearly represent the other. Each function can have its own "name". There will be no confusion, such as might be possible with both equations reading "y =".
(y = 3x + 2 and y = 4x - 6)
The most popular function notation is f (x) which is read "f of x".
This is NOT the multiplication of f times x.. |
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Traditionally, functions are referred to by single letter names, such as f, g, h and so on.
Any letter(s), however, may be used to name a function.
Examples:
 
The f (x) notation is another way of representing the output y-value in a function, y = f (x).
The y-axis may even be labeled as the f (x) axis, when graphing.
Ordered pairs may be written as (x, f (x)), instead of (x, y).
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Calculators graph functions! |
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Most calculators (including the TI-84+ series) can only handle graphing functions.
The equation (function) must be in "y = " form before you can enter it in the calculator.
By solving for "y =", you are actually identifying a "function".
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