Mississippi Math C.A.5

MathGrades 9–12Algebra (A) Demonstrate Basic Knowledge of Functions, Including their Behavior and Characteristics

The Standard

Investigate, describe, and determine asymptotic behavior using tables, graphs, and analytical methods

2025 Mississippi College- and Career-Readiness Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students use tables, graphs, and equations to find lines a function approaches. They describe what happens near a vertical asymptote and as x gets very large or very small.
What Mastery Looks Like: A student can find the vertical and horizontal asymptotes of y=(2x+1)/(x−3). They can explain why the graph falls without bound just left of x=3, rises without bound just right of it, and approaches y=2 far from x=3.
Common Misconceptions: Students may treat an undefined input as a point on the graph. They may call every denominator zero a vertical asymptote, even when a factor cancels and leaves a hole. Some think a graph can never cross a horizontal asymptote.
How to Assess It: Give students f(x)=(x+2)/(x−4). Ask them to calculate f(3.9), f(4.1), f(100), and f(−100), then name both asymptotes and explain the values.

Lesson moves

Use a calculator to fill a table for y=(2x+1)/(x−3) near x=3 and at x=±100, then plot the points on graph paper.
Compare (x−3)/(x−3) and (x+3)/(x−3) near x=3. Ask students to write why only one graph shoots up or down.
Match equation, graph, and table cards for y=1/x, y=1/(x−2), and y=(x−2)/(x−2), then label asymptotes and holes.
For shirts with a $60 setup fee plus $4 each, graph average cost (60+4n)/n and explain what it approaches as orders grow.

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