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Calculus practice

Evaluating Limits at Infinity with Graphs

Use equations with blank or completed coordinate graphs to evaluate exact polynomial, rational, exponential, and logarithmic limits at infinity.

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Use each equation and graph to evaluate the specified positive- or negative-infinity limit exactly.

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Paper sizes and printing help · More calculus activities

Connect formulas to visible tails

Students use the original equation with a blank or completed graph, then report an exact result for one specified direction.

Learning objective

What this activity builds

Connect exact symbolic end behavior with visible graph tails, holes, poles, and real-domain boundaries.

Worked example

Does a top-edge arrow prove the limit is positive infinity?

No. It only shows the curve continues beyond the viewing window.

Use the specified x-direction and equation to determine the true tail behavior.

Teaching notes

Make the practice count

  • Check which branch continues toward the requested infinity.
  • Keep removable holes separate from vertical asymptotes.
  • Use the equation for exact logarithmic constants.

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Choose 4 or 8 problems, any retained graph family, and blank or completed graphs. Every task always includes its equation.

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Math SheetNameScoreTeacherDateEvaluating Limits at Infinity with GraphsUse each equation and blank coordinate grid to sketch the function, then evaluate the specified limit exactly.1. Evaluate as x -> -infinity.f(x) =-1x-2-6-4-20246-8-6-4-22468xyExact limit:2. Evaluate as x -> +infinity.f(x) =-1+12·3-x+1-6-4-20246-8-6-4-22468xyExact limit:3. Evaluate as x -> +infinity.f(x) =2·x-1-6-4-20246-8-6-4-22468xyExact limit:4. Evaluate as x -> +infinity.f(x) =-1x2+4·x+4-6-4-20246-8-6-4-22468xyExact limit:Graph arrows show continuation beyond the viewing window.math-sheet.comPage 1 of 1

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