Limits from Graphs

Grade 10•45 minutes•The concept of a limit includes one sided limits. LIM-1.C.2 Graphical information about a function can be used to estimate limits. LIM-1.C.4 A limit might not exist for some functions at particular values of x. Some ways that the limit might not exist are if the function is unbounded, if the function is oscillating near this value, or if the limit from the left does not equal the limit from the right.

Learning Objective

I can identify from a graph when a limit does not exist due to unbounded behavior, oscillations, or differing one-sided limits.

Practice Questions

This lesson includes 7 practice questions to reinforce learning.

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1. Explain in your own words what it means for a limit to not exist at a particular x-value. Give three reasons, based on graphical behavior, why a limit might not exist.

2. Sketch a graph of a function where the limit as x approaches 1 from the left is 3, and the limit as x approaches 1 from the right is -1. What is the value of f(1) in your graph?

3. The graph of a function f(x) has a vertical asymptote at x = -2. a) If the limit as x approaches -2 from the left is -∞, and the limit as x approaches -2 from the right is ∞, does the limit as x approaches -2 exist? Explain. b) If the limit as x approaches -2 from the left is ∞, and the limit as x approaches -2 from the right is ∞, does the limit as x approaches -2 exist? Explain.

...and 4 more questions

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