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

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 expressions, graphs and tables in terms of the quantities, and sketch graphs showing key features given a description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Logarithmic Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Roots of a Quadratic
Slope-Intercept Form of a Line
Translating and Scaling Sine and Cosine 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.7a: Graph linear, quadratic and absolute value functions and show intercepts, maxima, minima and end behavior.

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.7b: Graph square root, cube root, and exponential functions.

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Radical Functions

F.IF.7c: Graph logarithmic functions, emphasizing the inverse relationship with exponentials and showing intercepts and end behavior.

Logarithmic Functions

F.IF.7d: Graph piecewise-defined functions, including step functions.

Absolute Value with Linear Functions

F.IF.7g: Graph trigonometric functions, showing period, midline, and amplitude.

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

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

F.IF.8a: Use different forms of linear functions, such as slope-intercept, standard, and point-slope form to show rate of change and intercepts.

Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

F.IF.8b: 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.9: Compare properties of two functions using a variety of representations (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: Use functions to model real-world relationships.

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

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

F.BF.2: Write arithmetic and geometric sequences and series 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: Transform parent functions (f(x)) by replacing f(x) with f(x) + k, kf(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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

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.4b: Read values of an inverse function from a graph or a table, given that the function has an inverse.

Logarithmic Functions

F.BF.4d: 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.LQE: Linear, Quadratic, and Exponential Models

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

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

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

Compound Interest

F.LQE.2: Construct exponential functions, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic 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.

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: 9/24/2019

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