BPS District Mathematics Standards

Math Learning Progressions

[F] Functions

Students’ prior knowledge includes:

  • Students define, evaluate and compare functions (grade 8)
  • Students use functions to model relationships between quantities (grade 8)
  • Students solve real-life and mathematical problems using numerical and algebraic expressions and equations (grade 7)
  • Students represent and analyze quantitative relationships between dependent and independent variables (grade 6)
Interpreting Functions
  • Understand the concept of a function and use function notation.
  • Interpret functions that arise in applications in terms of the context.
  • Analyze functions using different representations.
Building Functions
  • Build a function that models a relationship between two quantities.
  • Build new functions from existing functions.
Linear, Quadratic, and Exponential Models
  • Construct and compare linear, quadratic, and exponential models and solve problems.
  • Interpret expressions for functions in terms of the situation they model.
Trigonometric Functions
  • Extend the domain of trigonometric functions using the unit circle.
  • Model periodic phenomena with trigonometric functions.
  • Prove and apply trigonometric identities.

MAT-HS.F [F] Overview: Function

MAT-HS.F-IF Domain: [F-IF] Interpreting Functions

    • MAT-HS.F-IF.01 Understand that each element of the domain is exactly one element of the range
    • MAT-HS.F-IF.02 Use, evaluate, and interpret function notation in terms of a context
    • MAT-HS.F-IF.03 Recognize that sequences are functions whose domain is a subset of the integers
    • MAT-HS.F-IF.04 Interpret graphs of functions that model a relationship between 2 quantities
    • MAT-HS.F-IF.05 Relate the domain of a function to its graph and the relationship it describes
    • MAT-HS.F-IF.06 Calculate and interpret the average rate of change of a function
    • MAT-HS.F-IF.07 graph Functions expressed symbolically and show key features of the graph
      • MAT-HS.F-IF.07.a Graph linear functions and show intercepts.
      • F-IF.07.b Graph square root, cube root, and piecewisedefined functions
      • F-IF.07.c Graph polynomial functions
      • F-IF.07.d Graph rational functions
      • MAT-HS.F-IF.07.e Graph exponential and logarithmic functions
      • MAT-HS.F-IF.07.f graph a quadratic function and show intercepts, maxima and minima.
    • MAT-HS.F-IF.08 Write a function defined by an expression in different but equivalent forms
      • F-IF.08.a Use factoring and completing the square to show zeros/extreme values/symmetry
      • F-IF.08.b Use properties of exponents to interpret expressions for exponential functions
    • MAT-HS.F-IF.09 Compare properties of two Functions each represented in a different way

 

MAT-HS.F-BF Domain: [F-BF] Building Functions

    • MAT-HS.F-BF.01 Write a function that describes a relationship between two quantities
      • F-BF.01.a Determine an expression/recursive process/steps for calculation from context
      • F-BF.01.b Combine standard function types using arithmetic operations
      • F-BF.01.c Compose functions
    • MAT-HS.F-BF.02 Write arithmetic and geometric sequences, and translate between the two
    • MAT-HS.F-BF.03 Identify effects on a graph, replacing f(x) with f(x) + k, f(xk), k(fx), f(x+k)
    • MAT-HS.F-BF.04 Find inverse functions
      • F-BF.04.a Solve f(x)
      • F-BF.04.b Verify by composition that one function is the inverse of another
      • F-BF.04.c Read values of an inverse function from a graph or a table
      • F-BF.04.d Produce an invertible function from a noninvertible function
    • MAT-HS.F-BF.05 Understand the inverse relationship between exponents and logarithms

 

MAT-HS.F-LE Domain: [F-LE] Linear, Quadratic and Exponential Models*

    • MAT-HS.F-LE.01 Know when to use linear vs exponential functions
      • F-LE.01.a Prove linear functions grow by differences & exponential functions by factors
      • F-LE.01.b Recognize where a quantity changes at a constant rate relative to another
      • F-LE.01.c Recognize where a quantity grows/decays by constant percent relative to another
    • MAT-HS.F-LE.02 Construct linear and exponential functions given a graph/relationship/pairs
    • MAT-HS.F-LE.03 Observe that exponential increases are greater than linear increases
    • MAT-HS.F-LE.04 For exponential models, express as a logarithm the solution to ab^ct = d
    • MAT-HS.F-LE.05 Interpret parameters in a linear or exponential function in a context

 

MAT-HS.F-TF Domain: [F-TF] Trigonometric Functions

    • MAT-HS.F-TF.01 Understand radian measure of an angle
    • MAT-HS.F-TF.02 Explain how the unit circle enables trigonometric functions to all real numbers
    • MAT-HS.F-TF.03 Use special triangles to determine geometrically the values of sine, cosine
    • MAT-HS.F-TF.04 Use the unit circle to explain symmetry (odd and even)
    • MAT-HS.F-TF.05 Choose trigonometric functions to model periodic phenomena
    • MAT-HS.F-TF.06 Understand that restricting a trigonometric function to a domain on which i
    • MAT-HS.F-TF.07 Use inverse functions to solve trigonometric equations that arise in modeli
    • MAT-HS.F-TF.08 Prove the Pythagorean identity sin^2(?) + cos^2(?) = 1
    • MAT-HS.F-TF.09 Prove the addition and subtraction formulas for sine, cosine, and tangent a

 

A Sample of HS Math Concept Functions to Become Ready for College and Career

Interpreting Functions

  • Understand the concept of a function and use function notation.
  • Interpret functions that arise in applications in terms of the context.
  • Analyze functions using different representations.

Building Functions

  • Build a function that models a relationship between two quantities.
  • Build new functions from existing functions.

Linear, Quadratic, and Exponential Models

  • Construct and compare linear, quadratic, and exponential models and solve problems.
  • Interpret expressions for functions in terms of the situation they model.

Trigonometric Functions

  • Extend the domain of trigonometric functions using the unit circle.
  • Model periodic phenomena with trigonometric functions.
  • Prove and apply trigonometric identities.