Learning Resources

Investigation3: Discontinuities and Vertical Asymptotes

A function, f(x), is said to be continuous at a number c if all of the following three conditions are met.

1.  f(c) exists 
2. [i.e. ]
3. 

• If condition 1 fails, stop because the function is discontinuous at x = c. Otherwise, test condition 2. 
• If condition 2 fails, stop because the function is discontinuous at x = c. Otherwise, test condition 3.
• If condition 3 fails, then the function is discontinuous at x = c. Otherwise, the function is continuous at x = c.