Interpreting Functions 
HSF.IF: Analyze Functions Using Different Representations 
HSF.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.★ 

HSF.IF.7.a  Graph linear and quadratic functions and show intercepts, maxima, and minima. 

HSF.IF.7.b  Graph square root, cube root, and piecewisedefined functions, including step functions and absolute value functions. 

HSF.IF.7.c  Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. 

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

HSF.IF.7.e  Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. 

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

HSF.IF.8.a  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. 

HSF.IF.8.b  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. 

HSF.IF.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. 
Interpret Functions That Arise In Applications In Terms Of The Context 
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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.★ 

HSF.IF.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.★ 

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.★ 
Understand The Concept Of A Function And Use Function Notation 
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). 

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. 

HSF.IF.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. 
Linear, Quadratic, And Exponential Models 
HSF.LE: Construct And Compare Linear, Quadratic, And Exponential Models And Solve Problems 
HSF.LE.1  Distinguish between situations that can be modeled with linear functions and with exponential functions. 

HSF.LE.1.a  Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. 

HSF.LE.1.b  Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. 

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

HSF.LE.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). 

HSF.LE.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. 

HSF.LE.4  For exponential models, express as a logarithm the solution to abct =dwherea,c,anddarenumbersandthebasebis2,10,ore; evaluate the logarithm using technology. 
Interpret Expressions For Functions In Terms Of The Situation They Model 
HSF.LE.5  Interpret the parameters in a linear or exponential function in terms of a context. 