BPS District Mathematics Standards Book
Math Learning Progressions
[F] Functions
Math Learning Progressions HS Math Concepts
[F] Functions
Studentsâ€™ prior knowledge includes:
 Students define, evaluate and compare functions (grade 8)
 Students use functions to model relationships between quantities (grade 8)
 Students solve reallife 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.
MATHS.F [F] Overview: Function
MATHS.FIF Domain: [FIF] Interpreting Functions

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

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

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

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