F-IF: Interpreting Functions

F-IF.1: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Introduction to Functions
Points, Lines, and Equations

F-IF.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Absolute Value with Linear Functions
Translating and Scaling Functions

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.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

F-IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

General Form of a Rational Function
Introduction to Functions
Radical Functions
Rational Functions

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.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

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.

F-IF.7.a: Graph linear and quadratic functions and show intercepts, maxima, and minima.

Linear Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Slope-Intercept Form of a Line
Zap It! Game

F-IF.7.b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Absolute Value with Linear Functions
Radical Functions

F-IF.7.c: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

Graphs of Polynomial Functions
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form
Roots of a Quadratic
Zap It! Game

F-IF.7.d: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

General Form of a Rational Function
Rational Functions

F-IF.7.e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Cosine Function
Exponential Functions
Exponential Growth and Decay
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function

F-IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F-IF.8.a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

F-IF.11: Graph polar coordinates and curves. Convert between polar and rectangular coordinate systems.

Points in the Complex Plane

F-BF: Building Functions

F-BF.1: Write a function that describes a relationship between two quantities.

F-BF.1.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

Arithmetic Sequences
Geometric Sequences

F-BF.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Arithmetic Sequences
Geometric Sequences

F-BF.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

Exponential Functions
Logarithmic Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Zap It! Game

F-BF.4: Find inverse functions.

F-BF.4.b: Verify by composition that one function is the inverse of another.

Logarithmic Functions

F-BF.4.c: Read values of an inverse function from a graph or a table, given that the function has an inverse.

Logarithmic Functions

F-BF.5: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Logarithmic Functions

F-LE: Linear, Quadratic, and Exponential Models

F-LE.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.

F-LE.1.a: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

Compound Interest
Linear Functions

F-LE.1.b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

Arithmetic Sequences
Compound Interest
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Linear Functions

F-LE.1.c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

Drug Dosage
Exponential Growth and Decay
Half-life

F-LE.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

Compound Interest
Exponential Functions
Exponential Growth and Decay
Point-Slope Form of a Line
Slope-Intercept Form of a Line

F-LE.4: For exponential models, express as a logarithm the solution to ab to the c?? power = ?? where a, c, and ?? are numbers and the base b is 2, 10, or ??; evaluate the logarithm using technology.

Compound Interest
Logarithmic Functions

F-LE.5: Interpret the parameters in a linear or exponential function in terms of a context.

Arithmetic Sequences
Compound Interest
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Growth and Decay

F-TF: Trigonometric Functions

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.

Cosine Function
Sine Function
Tangent Function

F-TF.2.1: Graph all 6 basic trigonometric functions.

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

F-TF.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

Sound Beats and Sine Waves

F-TF.9: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine