Rate of change: 
Change in dependent variable with respect to change in independent variable.


In the function of y = f (x)

x is independent variable, y is the dependent variable.







Slope of secant:

Average rate of change of y with respect to x over the interval from x = a to x = a + h



Slope of tangent:
The slope of the tangent to the graph y = f (x) at point P (a, f(a))



If the slope of a line equal to m,
and then the slope of the line perpendicular to this line will be






Left hand limit:
Right hand limit: 




then there is a limit.


then limit does not exist






A function is continuous at a point when the graph passes through the point without a break.  If the graph has a break of some type at a point, then the graph is not continuous (discontinuous) at this point.


The function f (x) is continuous at x = a


If   = f (a)




Polynomial Functions:


P(x) = anxn + an-1xn-1 + ...a1x + a0


a0, a1, are constant.

All the polynomial functions are have limits at all real values.

All the polynomial functions are continuous at all real values.


Rational Functions:


      Every rational functions are continuous except at a value:  Q(a) = 0