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Intermediate Value Theorem worksheets

Check continuity and endpoint bracketing before making existence or no-guarantee conclusions.

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Check continuity and endpoint bracketing before making existence or no-guarantee conclusions.

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Method, assumptions, and units stay visible

Each generated problem includes bounded solvable givens. Worked pages show the theorem, formula, substitution, or physical slice used to reach the result.

Learning objective

What this activity builds

Use IVT hypotheses to make logically precise existence conclusions.

Worked example

What must be shown in a continuity solution?

The governing formula, substituted givens, and a labeled conclusion.

The worked key keeps the mathematical method visible rather than displaying only a result.

Teaching notes

Make the practice count

  • Keep units or domains beside each line.
  • Ask students to name the theorem or formula before substituting.
  • Distinguish exact values from labeled approximations.

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Math SheetNameScoreTeacherDateIntermediate Value Theorem ApplicationsCheck continuity on the closed interval, compare endpoint values with the target, and conclude only what the theorem guarantees.1.The endpoints of f(x)=x^2+15 on [-1,1] are both 16. Can IVT guarantee a point with f(c)=17?2.Let f(x)=x+12 for x<=1 and 2x+11 for x>1. Use IVT on [0,2] for target 13.State assumptions, domains, units, and approximation methods.math-sheet.comPage 1 of 3
Math SheetNameScoreTeacherDateIntermediate Value Theorem ApplicationsCheck continuity on the closed interval, compare endpoint values with the target, and conclude only what the theorem guarantees.3.For f(x)=1/(x-16), can IVT on [15,17] guarantee f(c)=0?4.For f(x)=1/(x+10), use IVT on [0,1] for target 0.0955.State assumptions, domains, units, and approximation methods.math-sheet.comPage 2 of 3
Math SheetNameScoreTeacherDateIntermediate Value Theorem ApplicationsCheck continuity on the closed interval, compare endpoint values with the target, and conclude only what the theorem guarantees.5.Let f(x)=x for x<0 and x+20 for x>=0. Can IVT on [-1,1] guarantee f(c)=0?6.For f(x)=x^2+13, use IVT on [0,3] to decide whether f(c)=15 is guaranteed.State assumptions, domains, units, and approximation methods.math-sheet.comPage 3 of 3

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