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Functions
Theory Refresher
 Click here for "Live" theory (132.7mb).
A function
is a rule that takes a real number and produces
another. The standard notation for a function is
where
Note that the variable used inside the brackets is not
important--it is the rule that matters.
Common names for functions are f, g, h.
Common variables used to express the rule are x, t and z.
To evaluate a function for some real number or
algebraic expression, simply substitute the real number (or
expression) into the rule for every occurrence of the variable given inside the
brackets (in the above case, t).
The zeroes or roots of
a function are the values of t that give
f(t)=0.
Two Special Cases
Linear Functions
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To find the zeroes, simply solve the equation ax + b = 0.
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Quadratic Functions
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There are three methods for finding zeroes.
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Domain and Range
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Domain
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The group of real numbers that can be put into the rule to obtain a valid result (sometimes it is the set of all real numbers).
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Range
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The group of real numbers that come out of the rule as the values in the domain are put into the rule.
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Operations
Functions can be added, subtracted, multiplied and divided.
Further, we can find the composition of two functions by
placing one inside the other. For two functions, f and
g, this is denoted by
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