Florida B.E.S.T. MA.912.C.1.6

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

The Standard

Decide when a limit is infinite and use limits involving infinity to describe asymptotic behavior.

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

Teacher's field guide

What Students Need to Do: Students analyze graphs, tables, and formulas to tell when function values increase or decrease without bound. They use one-sided and end-behavior limits to identify and describe asymptotes.
What Mastery Looks Like: Given a function, a student can state one-sided limits near a vertical asymptote and end-behavior limits. The student connects each result to the graph and uses correct infinity notation.
Common Misconceptions: Students may treat infinity as a number or assume the function reaches it. They may confuse vertical and horizontal asymptotes. They may substitute at a zero denominator and stop without checking one-sided behavior.
How to Assess It: Give f(x)=(2x+1)/(x-3). Ask students to find the limits as x approaches 3 from each side and as x approaches positive and negative infinity, then name the asymptotes.

Lesson moves

Place graph cards under three labels: vertical asymptote, horizontal asymptote, or neither, then write a supporting limit on each card.
Ask students to explain why infinity describes behavior rather than a point the function reaches.
Run an asymptote match game pairing formulas, graphs, limit statements, and vertical or horizontal asymptote cards.
Model average cost with C(x)=500/x+4, then have students explain why costs approach $4 as production grows.

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