1. Limits and Continuity

Connecting Multiple Representations Of Limits — Quiz

Test your understanding of connecting multiple representations of limits with 5 practice questions.

Practice Questions

Question 1

A graph shows that as $x$ gets close to $2$, the $y$-values of a function get close to $5$ from both sides. What is the limit of the function as $x\to 2$?

Question 2

A table of values shows $f(x)$ near $x=1$:
$$\begin{array}{c|c} x & f(x)\\hline 0.9 & 2.1\\ 0.99 & 2.01\\ 1.01 & 1.99\\ 1.1 & 1.9 \end{array}$$
What limit is suggested by the table?

Question 3

Which verbal description best matches the limit $\lim_{x\to 3} f(x)=4$?

Question 4

A function is defined by $f(x)=\begin{cases}2x+1, & x<4\\9, & x=4\\3x-3, & x>4\end{cases}$. What is $\lim_{x\to 4} f(x)$?

Question 5

A function has a hole at $x=5$, but the graph approaches $y=2$ from both sides as $x$ gets close to $5$. Which statement is true?