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 ax2+bx+c
Modeling the Factorization of x2+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 sin²(theta) + cos²(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