NY Next Generation Math AI-F.IF.7.b

MathGrades 9–12Graph functions and show key features of the graph by hand and by using technology where appropriate.

The Standard

Graph square root, and piecewise-defined functions, including step functions and absolute value functions and show key features.

New York State Next Generation Mathematics Learning Standards · Analyze functions using different representations.

Teacher's field guide

What Students Need to Do: Students graph square-root and piecewise functions in Algebra I, including step and absolute-value functions. They show intercepts, zeros, increasing or decreasing intervals, positive or negative intervals, extrema, and symmetry when present.
What Mastery Looks Like: The student respects domain endpoints and separate rules, plots accurate anchor points, and labels relevant features. Open and closed points, steps, vertices, and square-root starting points are shown correctly.
Common Misconceptions: Students may connect separate pieces, reverse open and closed endpoints, or extend a square-root graph beyond its real domain. They may confuse an absolute-value vertex with an intercept.
How to Assess It: Graph f(x) equals x plus 2 for x less than 0 and x squared for x greater than or equal to 0. Label endpoints, intercepts, and increasing intervals.

Lesson moves

Use string segments and endpoint tokens to build a piecewise graph on a floor coordinate grid.
Ask students how domain restrictions change the key features visible on a square-root or piecewise graph.
Play feature hunt across square-root, step, absolute-value, and piecewise graph cards.
Model shipping cost with a step function or distance from a location with an absolute-value function.

Keep exploring

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