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Reading & Writing Process

Students will use a variety of recursive reading and writing processes.

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Functions

Interpreting Functions

9-12.F-IF.4 - 9-12.F-IF.6 Interpret functions that arise in applications in terms of the context.

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9-12.F-IF.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship

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9-12.F-IF.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes

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9-12.F-IF.6

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified
interval. Estimate the rate of change from a graph

9-12.F-IF.7 - 9-12.F-IF.9 Analyze functions using different representations.

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9-12.F-IF.7

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology
for more complicated cases

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9-12.F-IF.8

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function

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9-12.F-IF.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions)

Building Functions

9-12.F-BF.1 Build a function that models a relationship between two quantities.

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9-12.F-BF.1

Write a function that describes a relationship between two quantities

9-12.F-BF.3 - 9-12.F-BF.4 Build new functions from existing functions.

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9-12.F-BF.3

Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs

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9-12.F-BF.4

Find inverse functions

Linear, Quadratic, and Exponential Models

9-12.F-LE.4 - 9-12.F-LE.4.3 Construct and compare linear, quadratic, and exponential models and solve problems.

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9-12.F-LE.4

For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology

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9-12.F-LE.4.1

Prove simple laws of logarithms

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9-12.F-LE.4.2

Use the definition of logarithms to translate between logarithms in any base

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9-12.F-LE.4.3

Understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values

Trigonometric Functions

9-12.F-TF.1 - 9-12.F-TF.2.1 Extend the domain of trigonometric functions using the unit circle.

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9-12.F-TF.1

Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle

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9-12.F-TF.2

Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle

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9-12.F-TF.2.1

Graph all 6 basic trigonometric functions

9-12.F-TF.5 Model periodic phenomena with trigonometric functions.

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9-12.F-TF.5

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline

9-12.F-TF.8 Prove and apply trigonometric identities.

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9-12.F-TF.8

Prove the Pythagorean identity sin2(θ ) + cos2(θ ) = 1 and use it to find sin(θ ), cos(θ ), or tan(θ ) given sin(θ ), cos(θ ), or tan(θ ) and the quadrant of the angle

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