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# L02 - Lecture 2 Functions Elementary Types A function is an...

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Lecture 2 — Functions, Elementary Types A function is an object having a rule that assigns to each element of a set A (called the domain) exactly one element of a set B (called the codomain). If the name of the function is f , then the element of B that is assigned to an element x from set A is denoted f ( x ) . This is NOT a multiplication, so you must be aware of the names of functions in use. The set of ALL the values f ( x ) for different x in A is called the range of the function. If the domain of a function f ( x ) is not explicitly stated, it is assumed to be all x for which there is a sensible f ( x ) value— we call it the (natural) domain of the function. For calculus, x and f ( x ) must be real. For applications, the domain may sometimes be smaller than the natural domain due to context.

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Consider these three different functions: f ( x ) = x 2 Q ( x ) = x 3 x Area ( x ) = x 2 , where x is the side of a square Find the domain of each function Θ( ω ) = 5 ω 4 + ω Γ( x ) = x 2 + x 2 - 5 x
Find the range of the function P ( t ) = 4 t 2 1 + t 2 Calculus will allow us to do this more easily and with more difficult functions.

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