Function (from a set X to a set Y):
A correspondence that associates with each element x (independent variable) of X and a unique element y (dependent variable) of Y. Notation: 
or 
.
Domain of a function:
The data set of all real numbers for which the correspondence makes sense.
One to one functions:
is a function from 
to 
.
Increasing functions:
If S is a subset of X and 
whenever
, in S, then 
is an increasing function in S.
Decreasing functions:
If S is subset of X and 
whenever
, in S, then 
is a decreasing function in S.
Slope:
If 
is a line which is not parallel to the 
-axis and if 
and 
are distinct points on
, then the slope 
of 
is given by:
.
Equation of a curve:
Suppose of a curve composed of points whose coordinates are 
for 
1, 2,….
If there is an equation
, by which all the 
can be calculated through substituting
, the equation 
is called the equation of the curve.
Equation of a line:
If the slope of a line is given (denoted by 
) and if a point on the line is given (coordinate is 
) , the line equation would be 
.
Vertical shifts:
If 
is a real number, the graph of 
is the graph of 
shifted upward 
units for 
or shifted downward for 
.
Horizontal shifts:
If 
is a real number, the graph of 
is the graph of 
shifted to the right 
units for 
or shifted to the left 
units for 
.
Reflection in the y-axis:
The graph of the function 
is the graph of 
reflected in the y-axis.
Reflection in the x-axis:
The graph of the function 
is the graph of 
reflected in the x-axis.
Vertical stretching and shrinking:
If 
is a real number, the graph of 
is the graph of 
stretched vertically by 
for 
or shrunk vertically by 
for 
.
Horizontal stretching and shrinking:
If 
is a real number, the graph of 
is the graph of 
stretched horizontally by 
for 
or shrunk horizontally by 
for 
.
Composite functions:
If 
is a function from 
to 
and 
is the function from 
to 
, then the composite function 
is the function from 
to 
defined by 
.
Inverse functions:
Let 
be a one to one function from 
to 
. Then, a function 
from 
to 
is called the inverse function of 
if 
for all 
in 
and 
for all 
in 
