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Math B
Functions and Relations
Notes
Relation – Any set that can be written as an ordered pair (x,y)
Domain - All of the x values of a relation
Range – All of the y values of a relation that correspond to the domain
Finite Set – Fixed number of ordered pairs
Infinite Set – A set that has a never ending set of ordered pairs
**** If no set or domain is specified, the domain would always be
the real numbers
FUNCTION - A relation that has one and only one y value for every x value
in the domain.
Functions - 1. A set is a function if it has no repeating x values
2. A Graph is a function if it passes the vertical line test
3. Even though a graph may not be a function, you can
Restrict the domain of the graph to make it a
function
Function Notation - y = , F(x), F:, F={(x,y)|,
Types of function - 1. Linear Functions - y = mx + b, Domain and Range
Is always real numbers except x = or y = lines
2. Quadratic Functions - y  ax  bx  c , Domain
Is always the Real numbers and the range depends
on the turning point.
2
3. Polynomial Functions - y  ax  .........
Where n is greater than 2. Domain is always
The real number and range depends on the power
of n.
n
4. Absolute Value Function – y = |x| , Domain is
All on the real numbers and the range is the
Positive real numbers.
5. Square Root Functions - y  x , Domain is the
Positive real numbers and the range is also the
Positive real numbers
6. Rational Functions – y 
x3
, Domain depends
x4
On the denominator and the range follows.
7. Rational Functions with a square root combination of 5 and 6.
One to one Functions - Has one y for every x and one x for every y.
Example: lines, square roots, some polynomial functions
Composite Functions - One Function inside of the other function.
Symbol - ( f  g )( x)  f ( g ( x))
Inverse Functions – If you do the composite of two functions and it comes
out to x.
Simple definition: Switch your x and y and resolve for inverse.