Mississippi Math A3.A.15
The Standard
Determine asymptotes and holes of rational functions, explain how each was found, and relate these behaviors to continuity.
2025 Mississippi College- and Career-Readiness Standards for Mathematics · Use Polynomials Identities to Solve Problems
Teacher's field guide
What This Standard Means
What Students Need to Do
- Factor rational functions to find denominator zeros that create holes or vertical asymptotes. Use end behavior to find horizontal or slant asymptotes. Explain where the function is not continuous and why.
What Mastery Looks Like
- For (x²−4)/(x²−x−2), a student finds a hole at (2, 4/3), a vertical asymptote at x=−1, and a horizontal asymptote at y=1. They explain that the function is not continuous at x=2 or x=−1, but only the hole can be filled.
Common Misconceptions
- Students may cancel a factor and forget that its zero is still excluded from the original function. They may call every denominator zero a vertical asymptote or think a graph cannot cross a horizontal asymptote.
How to Assess It
- Exit ticket: For (x²−1)/(x²−3x+2), find the hole and asymptotes. Explain how you found each one and name the x-values where the function is not continuous.
Lesson moves
Ways to Teach It
Give pairs graph paper to plot (x²−1)/(x−1) for x near 1, then mark the missing point with an open circle.
Ask students to explain in writing why canceling (x−1) in (x²−1)/(x−1) does not define a value at x=1.
Have pairs match cards showing (x²−4)/(x²−x−2), its hole (2, 4/3), and asymptotes x=−1 and y=1, then justify each match.
Graph cost per item, 2+50/x, for a $50 setup fee and $2 per item, then explain why x=0 is excluded.
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Printable A3.A.15 Worksheet
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