High School Functions (Alaska Standards)

Interpreting Functions

• F-IF.1 Know a function assigns each domain element exactly one range element; f(x) is the output for input x.
• F-IF.2 Use function notation, evaluate functions and interpret notation in context.
• F-IF.3 Recognize sequences as functions on the integers, sometimes defined recursively.
• F-IF.4 Interpret key graph and table features in context (intercepts, increase/decrease, maxima, symmetry, end behavior) and sketch graphs.
• F-IF.5 Link a function's domain to its graph and to the situation it models.
• F-IF.6 Calculate and interpret average rate of change over an interval and estimate it from a graph.
• F-IF.7 Graph functions from their equations and show key features, by hand or with technology.
• F-IF.8 Rewrite a function in equivalent forms to reveal different properties.
• F-IF.9 Compare properties of two functions shown in different ways.

Building Functions

• F-BF.1 Write a function for a relationship between two quantities.
• F-BF.2 Write arithmetic and geometric sequences recursively and explicitly, model with them and convert between forms.
• F-BF.3 Describe how adding k, multiplying by k or replacing x by kx or x + k changes a graph; find k; recognize even and odd functions.
• F-BF.4 Find inverse functions.
• F-BF.5 (+) Use the inverse link between exponents and logarithms to solve problems.

Linear, Quadratic, & Exponential Models

• F-LE.1 Tell situations modeled by linear functions from those modeled by exponential functions.
• F-LE.2 Build linear and exponential functions, including sequences, from a graph, a description or two input-output pairs.
• F-LE.3 Use graphs and tables to see that exponential growth eventually exceeds linear, quadratic or any polynomial growth.
• F-LE.4 Write solutions of ab^(ct) = d as logarithms (base 2, 10 or e) and evaluate them with technology.
• F-LE.5 Interpret the parameters of linear and exponential functions in context.

Trigonometric Functions

• F-TF.1 Understand radian measure as arc length on the unit circle.
• F-TF.2 Explain how the unit circle extends trigonometric functions to all real numbers.
• F-TF.3 (+) Use special triangles for sine, cosine and tangent of π/3, π/4 and π/6, and the unit circle for related angles.
• F-TF.4 (+) Use the unit circle to explain odd/even symmetry and periodicity of trigonometric functions.
• F-TF.5 Choose trigonometric functions to model periodic situations with given amplitude, frequency and midline.
• F-TF.6 (+) Know restricting a trigonometric function to a monotonic interval allows an inverse.
• F-TF.7 (+) Use inverse trigonometric functions to solve equations in modeling contexts and interpret the results.
• F-TF.8 Prove that sine squared plus cosine squared equals 1, then use it to find other trig values from one value and the quadrant.
• F-TF.9 (+) Prove and use the sine, cosine and tangent addition and subtraction formulas.