1) What is a discontinuity? How are discontinuities found? Which types of graphs are continuous?
3) If Bob starts off with a salary of $50,000 and earned $1000 a year for his salary, give the equation of his salary, S, for year t. Use this equation to find the year in which he would be earning $56,400. Show all your work using the equation.
From mathworld.com the definition of continuous is:
A general mathematical property obeyed by mathematical objects in which all elements are within a neighborhood of nearby points. The continuous maps between topological spaces form a category. The designation "continuous" is sometimes used to indicate membership in this category.
This means that a function f(x) is continuous if its value approach f(a) as x approaches a
In functions, we have three types of discontinuity:
1. The function is not defined at a certain point.
for example, look at the function:
As you can see, the function has a value everywhere except at x=0 in which we don't know what ...
Discontinuities, trends and forecasting are investigated in the following posting.