High School Functions (Colorado Academic Standards)

Standard 2: Algebra and Functions

• MA.HS.F-IF.A Understand functions and use function notation.
  • 1. Know a function assigns each domain element exactly one range element; f(x) is the output for input x.
  • 2. Use function notation, evaluate functions and interpret notation in context.
  • 3. Recognize sequences as functions on the integers, sometimes defined recursively.
• MA.HS.F-IF.B Interpret functions in context.
  • 1. Interpret key graph and table features in context (intercepts, increase/decrease, maxima, symmetry, end behavior) and sketch graphs.
  • 2. Link a function's domain to its graph and to the situation it models.
  • 3. Calculate and interpret average rate of change over an interval and estimate it from a graph.
• MA.HS.F-IF.C Analyze functions in different representations.
  • 1. Graph functions from their equations and show key features, by hand or with technology.
  • 1.a. Graph linear and quadratic functions showing intercepts, maxima and minima.
  • 1.b. Graph square root, cube root, piecewise, step and absolute value functions.
  • 1.c. Graph polynomial functions showing zeros and end behavior.
  • 1.d. (+) Graph rational functions showing zeros, asymptotes and end behavior.
  • 1.e. Graph exponential, logarithmic and trigonometric functions showing intercepts, end behavior, period, midline and amplitude.
  • 2. Rewrite a function in equivalent forms to reveal different properties.
  • 2.a. Factor or complete the square in a quadratic to show zeros, extreme values and symmetry, and interpret them.
  • 2.b. Use exponent properties to interpret exponential functions, e.g. as percent growth or decay.
  • 3. Compare properties of two functions shown in different ways.
• MA.HS.F-BF.A Build a function that models a relationship.
  • 1. Write a function for a relationship between two quantities.
  • 1.a. Find an explicit expression, recursive process or calculation steps from a context.
  • 1.b. Combine standard function types with arithmetic operations to model a situation.
  • 1.c. (+) Compose functions.
  • 2. Write arithmetic and geometric sequences recursively and explicitly, model with them and convert between forms.
• MA.HS.F-BF.B Build new functions from existing ones.
  • 1. 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.
  • 2. Find inverse functions.
  • 2.a. Solve f(x) = c for a simple invertible function and write its inverse.
  • 2.b. (+) Check by composition that two functions are inverses.
  • 2.c. (+) Read inverse-function values from a graph or table.
  • 2.d. (+) Make a function invertible by restricting its domain.
  • 3. (+) Use the inverse link between exponents and logarithms to solve problems.
• MA.HS.F-LE.A Build and compare linear, quadratic and exponential models and solve problems.
  • 1. Tell situations modeled by linear functions from those modeled by exponential functions.
  • 1.a. Prove linear functions grow by equal differences and exponential functions by equal factors over equal intervals.
  • 1.b. Recognize situations with a constant rate of change per unit.
  • 1.c. Recognize situations with a constant percent rate of growth or decay per unit.
  • 2. Build linear and exponential functions, including sequences, from a graph, a description or two input-output pairs.
  • 3. Use graphs and tables to see that exponential growth eventually exceeds linear, quadratic or any polynomial growth.
  • 4. Write solutions of ab^(ct) = d as logarithms (base 2, 10 or e) and evaluate them with technology.
• MA.HS.F-LE.B Interpret function expressions in terms of the situation.
  • 1. Interpret the parameters of linear and exponential functions in context.
• MA.HS.F-TF.A Extend trigonometric functions using the unit circle.
  • 1. (+) Understand radian measure as arc length on the unit circle. (being checked)
  • 2. (+) Explain how the unit circle extends trigonometric functions to all real numbers. (being checked)
  • 3. (+) Use special triangles for sine, cosine and tangent of π/3, π/4 and π/6, and the unit circle for related angles.
  • 4. (+) Use the unit circle to explain odd/even symmetry and periodicity of trigonometric functions.
• MA.HS.F-TF.B Model periodic situations with trigonometric functions.
  • 1. (+) Choose trigonometric functions to model periodic situations with given amplitude, frequency and midline. (being checked)
  • 2. (+) Know restricting a trigonometric function to a monotonic interval allows an inverse.
  • 3. (+) Use inverse trigonometric functions to solve equations in modeling contexts and interpret the results.
• MA.HS.F-TF.C Prove and apply trigonometric identities.
  • 1. (+) Prove that sine squared plus cosine squared equals 1, then use it to find other trig values from one value and the quadrant. (being checked)
  • 2. (+) Prove and use the sine, cosine and tangent addition and subtraction formulas.