Limits continuity

# Functions

A **function** f, is a relation between two sets with the property that each element in the first set is related *to exactly one* element in the second set.

A **real-valued or real function** is a function whose sets are the Real Numbers:

The

**domain**of a function is the subset of the initial set of the elements that have an image.The

**range or image**is the subset of the final set (or codomain) of the elements that are images of an element of the domain.Example 1:

it is not a function

Example 2:

Domain =

**R**Range = [-3,3]Example 3: Whole number portion function

Domain = **R** Range = **Z**

** **

**Exercise**: Decide if the following relations are functions or not, and if they are, find their domain and range:

a)

b)

c)

Solutions:

a) it's a function, dom = [-1,2]U[3,5)U(5,8], range = [0,5]

b) it's a function, dom = range = R

c) it is not a function

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