3. Calculus Foundations

Continuity — Quiz

Test your understanding of continuity with 5 practice questions.

Practice Questions

Question 1

Which of the following functions is continuous for all real values of x?

Question 2

A function $g(x)$ is defined as follows: $g(x) = \begin{cases} x^2 & x \leq 2 \\ 4x - 4 & x > 2 \end{cases}$. Is $g(x)$ continuous at $x = 2$?

Question 3

Which of the following types of discontinuities can be removed by redefining the function at a point?

Question 4

Consider the function $h(x) = \frac{x^2 - 4}{x - 2}$. What type of discontinuity does $h(x)$ have at $x = 2$?

Question 5

Which of the following conditions must hold for a function $f(x)$ to be continuous at a point $x = c$?