Academic Standards

KY.HS.F.1: Understand properties and key features of functions and the different ways functions can be represented.

KY.HS.F.1.a: 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.

Exponential Functions

Introduction to Functions

Linear Functions

Logarithmic Functions

Points, Lines, and Equations

Radical Functions

KY.HS.F.1.b: Using appropriate 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

Exponential Functions

Introduction to Exponential Functions

Points, Lines, and Equations

Quadratics in Polynomial Form

Radical Functions

KY.HS.F.1.c: 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

Cosine Function

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Exponential Functions

Function Machines 3 (Functions and Problem Solving)

General Form of a Rational Function

Graphs of Polynomial Functions

Introduction to Exponential Functions

Logarithmic Functions

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

Rational Functions

Sine Function

Tangent Function

KY.HS.F.1.d: 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

Logarithmic Functions: Translating and Scaling

Radical Functions

Rational Functions

KY.HS.F.1.e: 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

KY.HS.F.2: Recognize that arithmetic and geometric sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

KY.HS.F.3: Understand average rate of change of a function over an interval.

KY.HS.F.3.a: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval.

Cat and Mouse (Modeling with Linear Systems)

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Slope

KY.HS.F.3.b: Estimate the rate of change from a graph.

Cat and Mouse (Modeling with Linear Systems)

Slope

KY.HS.F.4: Graph functions expressed symbolically and show key features of the graph, with and without using technology (computer, graphing calculator).

KY.HS.F.4.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

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

KY.HS.F.4.b: Graph square root, cube root and absolute value functions.

Absolute Value Equations and Inequalities

Absolute Value with Linear Functions

Radical Functions

Translating and Scaling Functions

KY.HS.F.4.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

Roots of a Quadratic

Zap It! Game

KY.HS.F.4.d: Graph exponential and logarithmic functions, showing 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

KY.HS.F.4.e: Graph 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

KY.HS.F.4.f: Graph piecewise functions, including step functions.

Absolute Value with Linear Functions

Radical Functions

Translating and Scaling Functions

KY.HS.F.4.g: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available and showing end behavior.

General Form of a Rational Function

Rational Functions

KY.HS.F.5: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

KY.HS.F.5.a: Identify zeros, extreme values and symmetry of the graph within the context of a quadratic function.

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

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Roots of a Quadratic

Zap It! Game

KY.HS.F.5.b: Use the properties of exponents to interpret expressions for exponential functions and classify the exponential function as representing growth or decay.

Compound Interest

Exponential Functions

Exponential Growth and Decay

Introduction to Exponential Functions

KY.HS.F.6: Write a function that describes a relationship between two quantities.

KY.HS.F.6.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

KY.HS.F.6.b: Combine standard function types using arithmetic operations.

Addition and Subtraction of Functions

KY.HS.F.7: Use arithmetic and geometric sequences to model situations and scenarios.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

KY.HS.F.7.a: Use formulas (explicit and recursive) to generate terms for arithmetic and geometric sequences.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

KY.HS.F.7.b: Write formulas to model arithmetic and geometric sequences and apply those formulas in realistic situations.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

KY.HS.F.7.c: Translate between recursive and explicit formulas.

Arithmetic Sequences

Geometric Sequences

KY.HS.F.8: Understand the effects of transformations on the graph of a function.

KY.HS.F.8.a: 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.

Absolute Value with Linear Functions

Exponential Functions

Introduction to Exponential Functions

Logarithmic Functions

Logarithmic Functions: Translating and Scaling

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

Rational Functions

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Translations

Zap It! Game

KY.HS.F.8.b: 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

Logarithmic Functions

Logarithmic Functions: Translating and Scaling

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

Rational Functions

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Translations

Zap It! Game

KY.HS.F.9: Find inverse functions.

KY.HS.F.9.a: Given the equation of an invertible function, find the inverse.

KY.HS.F.9.c: Read values of an inverse function from a graph or a table, given that the function has an inverse.

KY.HS.F.9.d: Produce an invertible function from a non-invertible function by restricting the domain.

KY.HS.F.10: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents with the use of technology.

KY.HS.F.11: Distinguish between situations that can be modeled with linear functions and with exponential functions.

KY.HS.F.11.a: Recognize and justify that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.

Arithmetic and Geometric Sequences

Compound Interest

Direct and Inverse Variation

Exponential Functions

Introduction to Exponential Functions

Slope-Intercept Form of a Line

KY.HS.F.11.b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Compound Interest

Direct and Inverse Variation

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Linear Functions

Slope-Intercept Form of a Line

KY.HS.F.11.c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

Arithmetic and Geometric Sequences

Compound Interest

Exponential Growth and Decay

Geometric Sequences

KY.HS.F.12: 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

Exponential Growth and Decay

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

KY.HS.F.13: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

Arithmetic and Geometric Sequences

Compound Interest

Introduction to Exponential Functions

KY.HS.F.14: 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

Introduction to Exponential Functions

KY.HS.F.15: Understand the relationship of radian measure of an angle to its arc length.

Cosine Function

Sine Function

Tangent Function

KY.HS.F.16: Understand and use the unit circle.

KY.HS.F.16.a: 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

KY.HS.F.16.b: 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

KY.HS.F.16.c: 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

KY.HS.F.17: Choose trigonometric functions to model periodic phenomena with specified period, midline and amplitude.

Sound Beats and Sine Waves

Tides

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Waves

KY.HS.F.20: Proving identities and formulas within the context of trigonometry.

KY.HS.F.20.a: Prove the Pythagorean identity 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.

Cosine Function

Simplifying Trigonometric Expressions

Sine Function

Sine, Cosine, and Tangent Ratios

Tangent Function

KY.HS.F.20.b: 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: 9/15/2020

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.