NY Next Generation Math AI-F.IF.7

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

• AI-F.IF.7.b

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

01

What Students Need to Do

Students graph Algebra I linear, quadratic, exponential, square-root, absolute-value, step, and other piecewise functions by hand or with technology. They identify intercepts, zeros, extrema, intervals of change and sign, and symmetry where appropriate.

02

What Mastery Looks Like

The student selects a suitable window, produces an accurate graph, and labels features supported by the function type. Hand work and technology agree on key points and behavior.

03

Common Misconceptions

Students may trust a default window that hides features or connect points across a piecewise break. They may label an intercept, zero, extremum, or interval without checking its meaning.

04

How to Assess It

Give one quadratic and one piecewise function with two intervals. Ask students to graph both, label key features, and explain one technology-window choice.

1. 01

   Build graphs from key-point and feature cards before connecting only the intervals where the function is defined.

2. 02

   Ask students which graph features matter for each function family and why some features do not apply.

3. 03

   Run a graph-window challenge where teams adjust technology views to reveal hidden intercepts or extrema.

4. 04

   Graph a contextual linear, quadratic, exponential, or step model and interpret its most useful features.

• AII-F.IF.7

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

• NY-8.F.5

  Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a funct...