NY Next Generation Math AII-F.IF.7

MathGrades 9–12Analyze functions using different representations.

Standard Cluster

Graph functions and show key features of the graph by hand and using technology when appropriate.

New York State Next Generation Mathematics Learning Standards

Cluster contents

AII-F.IF.7 is a cluster heading. These are the individual standards under it.

Teacher's field guide

What Students Need to Do: Students graph Algebra II polynomial, cube-root, exponential, logarithmic, and trigonometric functions by hand or with technology. They display zeros and end behavior, intercepts, period, midline, and amplitude where appropriate.
What Mastery Looks Like: The student selects a revealing window, plots accurate anchor points, and labels features suited to the function family. Technology supports rather than replaces reasoning about behavior.
Common Misconceptions: Students may use one feature checklist for every family or accept a window that hides end behavior or periodic structure. They may confuse amplitude with vertical shift or period.
How to Assess It: Give one polynomial and one sinusoidal function. Ask students to graph both, label family-specific features, and justify the technology window used.

Lesson moves

Build family feature boards with anchor points, intercepts, end behavior, period, midline, and amplitude cards.
Ask students which features distinguish polynomial, logarithmic, and trigonometric graphs.
Run a graph-window challenge to reveal hidden zeros, end behavior, or full trigonometric cycles.
Graph a polynomial trend, exponential model, logarithmic scale, or periodic real-world signal.

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