Mississippi Math C.A.6

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

The Standard

Determine and justify the continuity and discontinuity of functions

2025 Mississippi College- and Career-Readiness Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students decide whether a function has a break at a given point. They compare what the function approaches from each side with its value at that point.
What Mastery Looks Like: Given a graph or piecewise rule, students can locate holes, jumps, and vertical asymptotes. They can explain why a function is or is not continuous at a point using limits and the function's value.
Common Misconceptions: Students may think a filled point makes a function continuous, even when the two sides approach different values. They may mistake a sharp corner for a break or miss a hole where the function is undefined.
How to Assess It: Exit ticket: Let f(x) = x + 2 for x < 1 and f(x) = 4 for x ≥ 1. Is f continuous at x = 1? Give the left limit, right limit, and f(1).

Lesson moves

Cut a printed graph of y = x + 2 at x = 1, slide the right half up one unit, and mark the endpoints.
Show y = x + 2 for x < 1 and y = x + 3 for x ≥ 1; ask students to explain what happens at x = 1.
Draw five graph cards showing a hole, jump, corner, vertical asymptote, and smooth curve; have pairs sort them as continuous or discontinuous.
Graph a parking fee of $4 through 60 minutes and $8 after 60 minutes, then explain the jump at one hour.

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