NY Next Generation Math AII-F.IF.7.e
The Standard
Graph cube root, exponential and logarithmic functions, showing intercepts and end behavior; and trigonometric functions, showing period, midline, and amplitude.
New York State Next Generation Mathematics Learning Standards · Analyze functions using different representations.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students graph cube-root, exponential, logarithmic, and trigonometric functions in Algebra II. They show intercepts and end behavior, and for sine, cosine, and tangent they identify period, midline, and amplitude when applicable.
What Mastery Looks Like
- The student uses correct anchor points and domain behavior for each family. Trigonometric graphs show the proper cycle and midline, while exponential and logarithmic graphs show intercepts and asymptotic behavior.
Common Misconceptions
- Students may treat inverse-looking families as reflections without checking, confuse asymptotes with intercepts, or assign tangent an amplitude. They may mix radians, degrees, and period scales.
How to Assess It
- Ask students to graph one logarithmic function and one transformed cosine function, labeling intercepts, end behavior, period, midline, and amplitude where applicable.
Lesson moves
Ways to Teach It
Place anchor-point and feature cards on blank cube-root, exponential, logarithmic, sine, cosine, and tangent axes.
Ask students which listed features apply to tangent and why amplitude does not.
Play family feature match with equations, graphs, intercepts, end behavior, period, midline, and amplitude.
Model sound, tides, pH, or population with a fitting Algebra II function family and graph.
Keep exploring
Related Standards
- AII-F.TF.4
Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
- AII-F.TF.5
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, horizontal shift, and midline.
- AI-F.IF.7.b
Graph square root, and piecewise-defined functions, including step functions and absolute value functions and show key features.
- AII-F.IF.7.c
Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
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