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 .
If S is a subset of X and whenever, in S, then is an increasing function in S.
If S is subset of X and whenever, in S, then is a decreasing function in S.
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 .
If is a real number, the graph of is the graph of shifted upward units for or shifted downward for .
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 .
If is a function from to and is the function from to , then the composite function is the function from to defined by .
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