F-IF: Interpreting Functions

1.1: Understand the concept of a function and use function notation

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).

 Absolute Value with Linear Functions
 Exponential Functions
 Introduction to Exponential Functions
 Introduction to Functions
 Linear Functions
 Logarithmic Functions
 Parabolas
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Quadratics in Vertex Form
 Radical Functions
 Standard Form of a Line

F-IF.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

 Arithmetic Sequences
 Geometric Sequences

1.2: Interpret functions that arise in applications in terms of the context

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.

 Absolute Value with Linear Functions
 Exponential Functions
 General Form of a Rational Function
 Graphs of Polynomial Functions
 Logarithmic Functions
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Quadratics in Vertex Form
 Radical Functions

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

 Introduction to Functions
 Logarithmic Functions
 Radical 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.

 Cat and Mouse (Modeling with Linear Systems)
 Slope

1.3: Analyze functions using different representations

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.

 Absolute Value with Linear Functions
 Cat and Mouse (Modeling with Linear Systems)
 Exponential Functions
 Linear Functions
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Quadratics in Vertex Form
 Roots of a Quadratic
 Slope-Intercept Form of a Line
 Standard 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
 Translating and Scaling 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
 Sine Function
 Tangent Function
 Translating and Scaling Sine and Cosine Functions

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.

 Modeling the Factorization of x2+bx+c
 Quadratics in Factored Form
 Quadratics in Vertex Form
 Roots of a Quadratic

F-IF.8.b: Use the properties of exponents to interpret expressions for exponential functions.

 Compound Interest
 Exponential Functions

F-IF.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

 General Form of a Rational Function
 Graphs of Polynomial Functions
 Linear Functions
 Logarithmic Functions
 Quadratics in Polynomial Form
 Quadratics in Vertex Form

F-BF: Building Functions

2.1: Build a function that models a relationship between two quantities

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
 Arithmetic and Geometric Sequences
 Geometric Sequences

F-BF.1.b: Combine standard function types using arithmetic operations.

 Addition and Subtraction of Functions

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
 Arithmetic and Geometric Sequences
 Geometric Sequences

2.2: Build new functions from existing functions

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.

 Absolute Value with Linear Functions
 Exponential Functions
 Introduction to Exponential Functions
 Rational Functions
 Translating and Scaling Functions
 Translating and Scaling Sine and Cosine Functions
 Translations
 Zap It! Game

F-BF.4: Find inverse 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.4.d: Produce an invertible function from a non-invertible function by restricting the domain.

 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

3.1: Construct and compare linear, quadratic, and exponential models and solve problems

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
 Direct and Inverse Variation
 Exponential Functions
 Introduction to Exponential Functions
 Slope-Intercept Form of a Line

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
 Direct and Inverse Variation
 Linear Functions
 Slope-Intercept Form of a Line

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

 Compound Interest

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).

 Absolute Value with Linear Functions
 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Compound Interest
 Exponential Functions
 Geometric Sequences
 Introduction to Exponential Functions
 Linear Functions
 Logarithmic Functions
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Slope-Intercept Form of a Line
 Standard Form of a Line

F-LE.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

 Compound Interest
 Introduction to Exponential Functions

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

 Logarithmic Functions

3.2: Interpret expressions for functions in terms of the situation they model

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

 Arithmetic Sequences
 Compound Interest
 Introduction to Exponential Functions

F-TF: Trigonometric Functions

4.1: Extend the domain of trigonometric functions using the unit circle

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.3: Use special triangles to determine geometrically the values of sine, cosine, tangent for pi/3, pi/4 and pi/6, and use the unit circle to express the values of sine, cosine, and tangent for pi - x, pi + x, and 2pi - x in terms of their values for x, where x is any real number.

 Cosine Function
 Sine Function
 Sum and Difference Identities for Sine and Cosine
 Tangent Function
 Translating and Scaling Sine and Cosine Functions

F-TF.4: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

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

4.2: Model periodic phenomena with trigonometric functions

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

 Translating and Scaling Functions
 Translating and Scaling Sine and Cosine Functions

4.3: Prove and apply trigonometric identities

F-TF.8: Prove the Pythagorean identity sinĀ²(theta) + cosĀ²(theta) = 1 and use it to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the angle.

 Simplifying Trigonometric Expressions
 Sine, Cosine, and Tangent Ratios

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

 Sum and Difference Identities for Sine and Cosine

Correlation last revised: 4/4/2018

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