Mississippi Math F-IF.7b

MathGrades 9–12Interpreting Functions

The Standard

F-IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

Graph square root and piecewise-defined functions, including absolute value functions.

2025 Mississippi College- and Career-Readiness Standards for Mathematics · Analyze Functions using Different Representations

Teacher's field guide

What Students Need to Do: Students graph square root, absolute value, and piecewise rules. They plot key points, use each rule only where it applies, and mark open or filled endpoints.
What Mastery Looks Like: Students place the start of a square root graph correctly and draw the sharp corner of an absolute value graph. They graph each piece on its stated interval, with open dots for excluded endpoints and filled dots for included endpoints.
Common Misconceptions: Some extend y=√x to negative inputs, where it has no real output. Others round the corner of an absolute value graph or put two filled dots at a piecewise boundary.
How to Assess It: Exit ticket: Graph f(x)=√x for 0≤x<4 and f(x)=|x−5| for x≥4, then mark the open and filled dots at x=4.

Lesson moves

Build squares with 1, 4, 9, and 16 tiles, then plot side length against tile count to sketch y=√x.
Graph f(x)=x+1 for x<2 and f(x)=5 for x≥2, then explain which dot at x=2 is filled.
Match rule cards for y=√x, y=|x−2|, and f(x)=0 if x<1 or 2 otherwise with graph cards, then explain one match.
Graph a bike rental fee: $8 for up to one hour, then $3 per hour after that, for rentals lasting up to four hours.

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