Calculus
Determining Continuity
Practice exact continuity intervals and one-sided-limit reasoning for piecewise, absolute-value, kinked-polynomial, and rational functions.
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Essential Discontinuity Limits from Graphs worksheets
Read signed one-sided and two-sided pole behavior from equations and accurate graphs.
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Use each equation or graph to evaluate the requested limit.
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Customize this worksheetApproach from each side
Every task keeps the original equation, domain and point value separate from its exact one-sided behavior.
Learning objective
What this activity builds
Connect pole equations to their one-sided graph behavior.
Worked example
At x = a, the left branch approaches 2 and the right branch approaches -1. Find all three limits.
The one-sided limits are 2 and -1; the two-sided limit is DNE.
Unequal one-sided limits prevent a two-sided limit, regardless of f(a).
Teaching notes
Make the practice count
- Read the approach direction before evaluating.
- Keep signed infinity separate from finite real limits.
- Check open and closed graph endpoints independently.
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Exact one-sided behavior drives both the equation and graph presentations.
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Related activities
Calculus
Determining Continuity from Graphs
Read completed graphs or sketch exact piecewise, absolute-value, kinked-polynomial, and rational functions before finding continuity intervals.
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