Learning Standards

OH.Math.HSF.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

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

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

OH.Math.HSF.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

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

Arithmetic Sequences

Geometric Sequences

OH.Math.HSF.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

Function Machines 3 (Functions and Problem Solving)

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

1.2.1.1: Key features include the following: 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

Exponential Functions

Function Machines 3 (Functions and Problem Solving)

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

OH.Math.HSF.IF.4a: Focus on linear and exponential functions.

Absolute Value with Linear Functions

Exponential Functions

Graphs of Polynomial Functions

Linear Functions

Logarithmic Functions

Slope-Intercept Form of a Line

OH.Math.HSF.IF.4b: Focus on linear, quadratic, and exponential functions.

Absolute Value with Linear Functions

Exponential Functions

Graphs of Polynomial Functions

Linear Functions

Logarithmic Functions

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Slope-Intercept Form of a Line

OH.Math.HSF.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

Logarithmic Functions

Radical Functions

Rational Functions

OH.Math.HSF.IF.5a: Focus on linear and exponential functions.

Exponential Functions

Logarithmic Functions

OH.Math.HSF.IF.5b: Focus on linear, quadratic, and exponential functions.

Exponential Functions

Logarithmic Functions

OH.Math.HSF.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

OH.Math.HSF.IF.7: Graph functions expressed symbolically and indicate key features of the graph, by hand in simple cases and using technology for more complicated cases. Include applications and how key features relate to characteristics of a situation, making selection of a particular type of function model appropriate.

OH.Math.HSF.IF.7a: Graph linear functions and indicate intercepts.

Absolute Value with Linear Functions

Cat and Mouse (Modeling with Linear Systems)

Exponential Functions

Graphs of Polynomial Functions

Linear Functions

Point-Slope Form of a Line

Points, Lines, and Equations

Polynomials and Linear Factors

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

OH.Math.HSF.IF.7b: Graph quadratic functions and indicate intercepts, maxima, and minima.

Absolute Value with Linear Functions

Exponential Functions

Graphs of Polynomial Functions

Linear Functions

Point-Slope Form of a Line

Points, Lines, and Equations

Polynomials and Linear Factors

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

OH.Math.HSF.IF.7c: 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

OH.Math.HSF.IF.7d: Graph polynomial functions, identifying zeros, when factoring is reasonable, and indicating end behavior.

Graphs of Polynomial Functions

Polynomials and Linear Factors

Quadratics in Factored Form

Roots of a Quadratic

Zap It! Game

OH.Math.HSF.IF.7e: Graph simple exponential functions, indicating intercepts and end behavior.

Cosine Function

Exponential Functions

Introduction to Exponential Functions

Logarithmic Functions

Logarithmic Functions: Translating and Scaling

Sine Function

Tangent Function

Translating and Scaling Sine and Cosine Functions

OH.Math.HSF.IF.7f: Graph exponential functions, indicating intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Cosine Function

Exponential Functions

Introduction to Exponential Functions

Logarithmic Functions

Logarithmic Functions: Translating and Scaling

Sine Function

Tangent Function

Translating and Scaling Sine and Cosine Functions

OH.Math.HSF.IF.7g: Graph rational functions, identifying zeros and asymptotes when factoring is reasonable, and indicating end behavior.

General Form of a Rational Function

Rational Functions

OH.Math.HSF.IF.7h: Graph logarithmic functions, indicating intercepts and end behavior.

Cosine Function

Exponential Functions

Introduction to Exponential Functions

Logarithmic Functions

Logarithmic Functions: Translating and Scaling

Sine Function

Tangent Function

Translating and Scaling Sine and Cosine Functions

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

OH.Math.HSF.IF.8a: 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 *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Quadratics in Factored Form

Quadratics in Vertex Form

OH.Math.HSF.IF.8b: Use the properties of exponents to interpret expressions for exponential functions.

Compound Interest

Exponential Functions

OH.Math.HSF.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

OH.Math.HSF.IF.9a: Focus on linear and exponential functions.

OH.Math.HSF.IF.9b: Focus on linear, quadratic, and exponential functions.

Exponential Functions

Graphs of Polynomial Functions

Quadratics in Polynomial Form

OH.Math.HSF.BF.1: Write a function that describes a relationship between two quantities.

OH.Math.HSF.BF.1a: Determine an explicit expression, a recursive process, or steps for calculation from context.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

OH.Math.HSF.BF.1a.i: Focus on linear and exponential functions.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

Introduction to Exponential Functions

OH.Math.HSF.BF.1a.ii: Focus on situations that exhibit quadratic or exponential relationships.

Arithmetic and Geometric Sequences

Geometric Sequences

Introduction to Exponential Functions

OH.Math.HSF.BF.1b: Combine standard function types using arithmetic operations.

Addition and Subtraction of Functions

OH.Math.HSF.BF.1c: Compose functions.

Function Machines 1 (Functions and Tables)

OH.Math.HSF.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

OH.Math.HSF.BF.3: Identify the effect on the graph of replacing f(x) by 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

Logarithmic Functions

Logarithmic Functions: Translating and Scaling

Quadratics in Vertex Form

Radical Functions

Rational Functions

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Translations

Zap It! Game

OH.Math.HSF.BF.3a: Focus on transformations of graphs of quadratic functions, except for f(kx).

Absolute Value with Linear Functions

Exponential Functions

Introduction to Exponential Functions

Quadratics in Vertex Form

Rational Functions

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Translations

Zap It! Game

OH.Math.HSF.BF.4: Find inverse functions.

OH.Math.HSF.BF.4a: Informally determine the input of a function when the output is known.

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

Function Machines 3 (Functions and Problem Solving)

Logarithmic Functions

OH.Math.HSF.BF.4c: Verify by composition that one function is the inverse of another.

OH.Math.HSF.BF.4d: Find the inverse of a function algebraically, given that the function has an inverse.

OH.Math.HSF.BF.4e: Produce an invertible function from a non-invertible function by restricting the domain.

OH.Math.HSF.BF.5: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

OH.Math.HSF.LE.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.

OH.Math.HSF.LE.1a: Show 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

Exponential Growth and Decay

Introduction to Exponential Functions

Linear Functions

Slope-Intercept Form of a Line

OH.Math.HSF.LE.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

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

Compound Interest

Exponential Growth and Decay

OH.Math.HSF.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

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 3 (Functions and Problem Solving)

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

OH.Math.HSF.LE.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically.

Compound Interest

Introduction to Exponential Functions

OH.Math.HSF.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.

Compound Interest

Logarithmic Functions

OH.Math.HSF.LE.5: Interpret the parameters in a linear or exponential function in terms of a context.

Arithmetic Sequences

Compound Interest

Exponential Growth and Decay

Introduction to Exponential Functions

OH.Math.HSF.TF.1: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Sine Function

Tangent Function

OH.Math.HSF.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

OH.Math.HSF.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

OH.Math.HSF.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

OH.Math.HSF.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

OH.Math.HSF.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

OH.Math.HSF.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

Correlation last revised: 9/15/2020