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Jump Discontinuity Limits from Graphs worksheets

Read finite one-sided limits and endpoint values from piecewise graphs.

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Use each equation or graph to find both one-sided limits and the two-sided limit.

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Approach 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

Interpret open and closed endpoints without replacing limits by point values.

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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Math SheetNameScoreTeacherDateJump Discontinuity Limits from GraphsUse the equation or graph to find both one-sided limits and the two-sided limit.1.f(x) =4, x < -16, x > -1-4-3-2-11234-8-6-4-22468limx -> -1-f(x) = ________________limx -> -1+f(x) = ________________limx -> -1f(x) = ________________2.f(x) = -2 - |x|x-4-3-2-11234-8-6-4-22468limx -> 0-f(x) = ________________limx -> 0+f(x) = ________________limx -> 0f(x) = ________________3.f(x) =-x+3, x < 1-x+2, x > 1f(1) = 2-4-3-2-11234-8-6-4-22468limx -> 1-f(x) = ________________limx -> 1+f(x) = ________________limx -> 1f(x) = ________________4.f(x) = -1 - 2|x + 2|x + 2-4-3-2-11234-8-6-4-22468limx -> -2-f(x) = ________________limx -> -2+f(x) = ________________limx -> -2f(x) = ________________Keep one-sided limits, two-sided limits, and f(a) distinct.math-sheet.comPage 1 of 1

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