NY Next Generation Math AII-F.IF.9
MathGrades 9–12Analyze functions using different representations.
The Standard
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students compare two functions shown in different representations. They extract comparable features such as intercepts, rate of change, extrema, end behavior, or periodic features before making a claim.
What Mastery Looks Like
- The student compares a table with a graph or equation using two accurate properties. The comparison works across polynomial, radical, exponential, logarithmic, or trigonometric functions.
Common Misconceptions
- Students may compare surface features that use different scales or inputs. They may assume a graph and table describe the same function because a few values match.
How to Assess It
- Provide one function as a graph and another as a table. Ask for two supported comparisons and one limitation of the available representations.
Lesson moves
Ways to Teach It
Post graph, table, equation, and description cards; students extract the same feature from each representation.
Ask which representation gives the strongest evidence for comparing end behavior and why.
Play function comparison bingo with intercept, maximum, period, growth, and domain clues.
Compare two population models presented as a data table and a verbal forecast.
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