4. Calculus Foundations

Continuity — Quiz

Test your understanding of continuity with 5 practice questions.

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Practice Questions

Question 1

Which of the following conditions is NOT required for a function $f(x)$ to be continuous at a point $x = c$?

Question 2

Consider the function $f(x) = \frac{1}{x}$. Which of the following statements about its continuity is true?

Question 3

What type of discontinuity is characterized by the left-hand limit and the right-hand limit existing but not being equal at a certain point?

Question 4

For a function $f(x)$ to be continuous on an open interval $(a, b)$, which of the following must be true?

Question 5

Given the function $f(x) = \begin{cases} x + 3 & \text{if } x < 2 \\ kx - 1 & \text{if } x \ge 2 \end{cases}$. For what value of $k$ is $f(x)$ continuous at $x = 2$?