Florida B.E.S.T. MA.912.C.1.5

MathGrades 9–12Develop an understanding for limits and continuity. Determine limits and continuity.

The Standard

Find limits at infinity.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students determine what function values approach as inputs grow without bound in either direction. They use graphs, tables, or dominant terms to support the result.
What Mastery Looks Like: Students find limits as x approaches positive or negative infinity from formulas, graphs, and tables. They use dominant terms correctly and state when a limit is finite, infinite, or nonexistent.
Common Misconceptions: Students may treat infinity as a number and try direct substitution. They may compare all terms instead of dominant terms, or assume both ends behave the same way.
How to Assess It: Give this exit ticket: Find both end limits of f(x) = (3x² - 2)/(x² + 5), then justify using dominant terms.

Lesson moves

Use a graphing calculator to make tables for large positive and negative inputs, then compare each function's end behavior.
Ask students to explain why lower-degree terms matter less as the input grows, using one rational function as evidence.
Play a card sort matching function formulas, graphs, dominant-term comparisons, and limits at positive and negative infinity.
Model long-term medication concentration with C(t) = 20t/(t + 4), then interpret the limit in context.

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