Prompt #2

For this week’s prompt we have to explain how to find three different types of discontinuities. The three types of discontinuities are a jump, removable, and a vertical asymptote. I guess I will start of by explaining how to know if something is continuous or not. For something to be continuous the left and the right side must be approaching the same number, and if a limit exists, it must be equal to a function value at that point. However, jumps, removables, and vertical asymptotes, are discontinuities and I’ll explain why.

1. Jump
The easiest way to see if a function has a discontinuity is to graph it. When graphing it, if there is a jump in the graph, or a point when the graph will break from one number to another it would be classified as a jump. -How to figure it out without looking at the graph? If the function is x=# and it takes on a different value, it is usually a jump. *A jump could be put in a piecewise function.

2. Removable
There are several ways to find out if a removable has a discontinuity. One way is to try and solve a function. The steps would be: factor and cancel. Take what you cancelled and set it equal to zero. Whatever answer you get (x=#) that would be the removable. In a graph, a removable discontinuity is a point at which a graph is not connected. There will be an open circle at the point where there is a removable.

3. Vertical Asymptote
**Vertical asymptotes occur when it is undefined, infinity, or negative infinity. You can do two things to see if a vertical asymptote has a discontinuity. When graphing the function, the number that does not get touched by the vertical asymptotes will be the discontinuity. When solving without your calculator, follow the same steps as a removable. Except set what is left in the bottom equal to zero. X=# will be the discontinuity.