Mississippi Math A3.G.37

MathGrades 9–12Geometry (G) Recognize, Sketch, and Transform Graphs to Functions

The Standard

Graph piecewise-defined functions and determine continuity or discontinuities.

2025 Mississippi College- and Career-Readiness Standards for Mathematics · Prove and Apply Trigonometric Identities

Teacher's field guide

What Students Need to Do: Students graph each rule only where it applies and mark boundary points with open or filled dots. They compare what the graph approaches from each side with its value at the boundary. They decide whether the graph connects, jumps, or has a hole.
What Mastery Looks Like: A student plots each piece on the correct interval and marks the boundary dots correctly. They use both sides of the graph and the value at the boundary to explain whether it is continuous.
Common Misconceptions: Students may extend every rule across the whole grid or swap open and filled dots. Some think two straight pieces must connect, even when they reach different heights. Others check only whether the sides meet and forget to check the value at the boundary.
How to Assess It: Exit ticket: Graph f(x)=x+1 for x<2 and f(x)=2x for x≥2. Mark the boundary dots, then state whether the function is continuous at x=2 and give the value approached from each side.

Lesson moves

Lay two colored paper strips along y=x+1 for x<2 and y=2x for x≥2 on a grid; add open and filled dots.
Write two sentences explaining why a filled dot at (2,5) breaks continuity when both sides of the graph approach (2,3).
Match graph cards to rule cards using y=x+1 for x<2 and either y=2x or y=5-x for x≥2; label each graph continuous or discontinuous.
Sketch parking fees: $3 for 0<t≤1 hour and $6 for 1<t≤2 hours; mark the discontinuity at t=1.

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