Maryland Math F.IF.C.7.f

MathGrades 9–12INTERPRETING FUNCTIONS

The Standard

F.IF.C.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 all functions including piecewise-defined functions, step functions and absolute value functions

Maryland College and Career Ready Standards for Mathematics (2025) · Analyze functions using different representations.

Teacher's field guide

What Students Need to Do: Students graph functions from equations or tables, using points and the rule to draw each part. They graph piecewise and step rules on the right intervals, mark endpoints, and locate the vertex of an absolute value graph.
What Mastery Looks Like: Given y=|x−2|, a student places the vertex at (2,0) and plots points on both sides. For a piecewise or step rule, they draw each part only where it applies and use open or filled dots at the boundaries.
Common Misconceptions: Students may connect pieces across a jump or put filled dots on both pieces at the same boundary. They may draw an absolute value graph as one straight line or slope a step graph between levels.
How to Assess It: Ask students to graph y=x for x<1 and y=2 for x≥1. Have them mark both endpoints at x=1 and explain which point belongs to the graph.

Lesson moves

Use two colored pencils on graph paper to plot y=x for x<1 and y=2 for x≥1, then mark both endpoints.
Ask, “Why is (1,1) open and (1,2) filled in this piecewise graph?”
Give pairs graph cards and rule cards for y=|x−2|, y=x², and a two-level step function; have them match and explain.
Graph a parking fee of $4 for 0<x≤1 hour and $7 for 1<x≤2 hours; mark both dots at one hour.

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