1. Limits and Continuity

Estimating Limit Values From Graphs — Quiz

Test your understanding of estimating limit values from graphs with 5 practice questions.

Practice Questions

Question 1

If the graph of a function gets closer and closer to $y=3$ as $x$ approaches $2$ from both sides, what is the best estimate for $\lim_{x\to 2} f(x)$?

Question 2

A graph has a hole at $x=1$ located at the point $\left(1,4\right)$, and the curve approaches that hole from both sides. What is the estimated value of $\lim_{x\to 1} f(x)$?

Question 3

If the left-hand behavior of a graph approaches $2$ as $x\to 0^-$ and the right-hand behavior approaches $5$ as $x\to 0^+$, what can be concluded about $\lim_{x\to 0} f(x)$?

Question 4

A graph rises without bound as $x$ gets close to $3$ from the right. What is the best description of $\lim_{x\to 3^+} f(x)$?

Question 5

Which graph feature most strongly suggests that a limit may exist at a point even if the function is not defined there?