Standard 
Lessons 
Worksheets/Games 
HSFIF.A.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). 
Domain of a function 

HSFIF.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 
Understanding function notation 

HSFIF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n1) for n ≥ 1. 

HSFIF.B.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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 
Interpreting features of functions 

HSFIF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of personhours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. 
Domain and range from graph 

HSFIF.B.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. 

HSFIF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. 
See Below 
Graphing linear equations Line graph intuition Linear function intercepts 
HSFIF.C.7a Graph linear and quadratic functions and show intercepts, maxima, and minima. 
Graphing parabolas in standard form 

HSFIF.C.7b Graph square root, cube root, and piecewisedefined functions, including step functions and absolute value functions. 
Graph
Square Root & Cube Root Functions 
Graphs of radical functions 
HSFIF.C.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. 

HSFIF.C.7d (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. 

HSFIF.C.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. 
Graph Exponential & Logarithmic
Functions 
Features of trigonometric functions 
HSFIF.C.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. 
See Below 
Rewriting quadratic expressions 
HSFIF.C.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. 
Solve Quadratics by Factoring 

HSFIF.C.8b Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^{t}, y = (0.97)^{t}, y = (1.01)^{12t}, y = (1.2)^{t/10}, and classify them as representing exponential growth or decay. 

HSFIF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 
Standard 
Lessons 
Worksheets/Games 
HSFBF.A.1 Write a function that describes a relationship between two quantities. 
See Below 

HSFBF.A.1a Determine an explicit expression, a recursive process, or steps for calculation from a context. 

HSFBF.A.1b Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 
Modeling with onevariable equations and inequalities 

HSFBF.A.1c (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time. 
Evaluate Composite Functions 

HSFBF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 

HSFBF.B.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. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 

HSFBF.B.4 Find inverse functions. 
See Below 

HSFBF.B.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2x^{3} or f(x) = (x+1)/(x?1) for x ≠ 1. 
Inverses of linear functions 

HSFBF.B.4b (+) Verify by composition that one function is the inverse of another. 
Understand inverses of functions 

HSFBF.B.4c (+) Read values of an inverse function from a graph or a table, given that the function has an inverse. 
Understand inverses of functions 

HSFBF.B.4d (+) Produce an invertible function from a noninvertible function by restricting the domain. 
Understand inverses of functions 

HSFBF.B.5 (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. 
Evaluating logarithms 
Standard 
Lessons 
Worksheets/Games 
HSFLE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. 

HSFLE.A.1a Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. 
Understand linear and exponential models 

HSFLE.A.1b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. 
Understand linear and exponential models 

HSFLE.A.1c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. 
Understand linear and exponential models 

HSFLE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). 

HSFLE.A.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. 
Compare growth rates of exponentials and polynomials 

HSFLE.A.4 For exponential models, express as a logarithm the solution to ab^{c} = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. 
Use logarithms to solve exponential equations 

HSFLE.B.5 Interpret the parameters in a linear or exponential function in terms of a context. 
Standard 
Lessons 
Worksheets/Games 
HSFTF.A.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. 

HSFTF.A.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. 

HSFTF.A.3 (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for x, π + x, and 2π ? x in terms of their values for x, where x is any real number. 

HSFTF.A.4 (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. 
Symmetry and periodicity of trigonometric functions 

HSFTF.B.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. 
Modeling with periodic functions Modeling with periodic functions 2 

HSFTF.B.6 (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. 

HSFTF.B.7 (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. 

HSFTF.C.8 Prove the Pythagorean identity sin^{2}(θ) + cos^{2}(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. 

HSFTF.C.9 (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. 
Addition and subtraction trig identities 
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with stepbystep explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.