Limit and Continuity Graphs: Practice Questions

Use the following figure to answer the practice problems.

A pretty bizarre graph.

Practice questions

1. f(5) = ?
2. f(18) = ?
3. List the x coordinates of all discontinuities of f, state whether the discontinuities are removable or nonremovable, and give the type of discontinuity—hole, jump, or infinite.

Answers and explanations

1. f(5) = 4, the height of the solid dot at x = 5.
2. f(18) is undefined because f has no y value corresponding to the x value of 18.
3. At x = –7, the vertical asymptote, there is a nonremovable, infinite discontinuity. At x = 5, there’s a nonremovable, jump discontinuity. At x = 13 and x = 18, there are holes which are removable discontinuities.

Though infinitely small, these are nevertheless discontinuities. They’re “removable” discontinuities because you can “fix” the function by plugging the holes.