Question 207222
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Think of a function like a box that has a slot on one end, a hopper on the other end, and a hand crank in the middle.  You put values into the slot (the *[tex \Large x] values) and turn the crank.  The function box then applies the rule that defines that function, and a function value (the *[tex \Large y] values) comes out in the hopper.


The domain of a function is the set of values that you are allowed to put into the slot.  Some functions allow you to put any value into them and get a valid answer out the other end, while other functions restrict you from putting in certain values.


For example, you would restrict the domain for any value that would cause a denominator in the function to equal zero; as in the situation where you had *[tex \Large x - 3] in a denominator in the function definition, you would not allow the value 3 to be included in the domain.  There are other situations where you must restrict the domain in other ways -- it just depends on the particular function and over what set of numbers you want the function defined.


While we're at it, let's also discuss the range of a function.  The range is the set of numbers that could possibly come out of the output hopper for all possible elements contained in the domain.



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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