1. Limits and Continuity

Continuity Basics — Quiz

Test your understanding of continuity basics with 5 practice questions.

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Practice Questions

Question 1

Which of the following conditions is essential for a function to be continuous on a closed interval $[a, b]$?

Question 2

Consider the function $f(x) = \frac{x^2 - 1}{x - 1}$. What type of discontinuity does $f(x)$ have at $x=1$?

Question 3

If a function $f(x)$ is continuous on the interval $[2, 7]$ and $f(2) = -3$ and $f(7) = 5$, which of the following values is guaranteed to be taken by $f(x)$ at some point $c$ in $(2, 7)$ by the Intermediate Value Theorem (IVT)?

Question 4

Which of the following functions has an infinite discontinuity at $x=0$?

Question 5

For what value of $c$ is the function $f(x) = \begin{cases} cx + 2 & \text{if } x < 3 \\ x^2 - c & \text{if } x \ge 3 \end{cases}$ continuous at $x=3$?