F.IF

Interpreting Functions

F.IF.1(all) 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).F.IF.2(all) Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.F.IF.3(9/10/11) Recognize patterns in order to write functions whose domain is a subset of the integers. (9/10) Limited to linear and quadratic. For example, find the function given {(−1,4),(0,7),(1,10),(2,13)}.F.IF.4(all) For a function that models a relationship between two quantities, interpret key features of expressions, graphs and tables in terms of the quantities, and sketch graphs showing key features given a 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.F.IF.5(all) 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 person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.F.IF.6(9/10/11) 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. (9/10) limited to linear functions.F.IF.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.F.IF.7a(9/10) Graph linear, quadratic and absolute value functions and show intercepts, maxima, minima and end behavior.F.IF.7b(11) Graph square root, cube root, and exponential functions.F.IF.7c(11) Graph logarithmic functions, emphasizing the inverse relationship with exponentials and showing intercepts and end behavior.F.IF.7d(+) Graph piecewise-defined functions, including step functions.F.IF.7e(11) Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.F.IF.7f(+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.F.IF.7g(+) Graph trigonometric functions, showing period, midline, and amplitude.F.IF.8Write a function in different but equivalent forms to reveal and explain different properties of the function.F.IF.8a(9/10) Use different forms of linear functions, such as slope-intercept, standard, and point-slope form to show rate of change and intercepts.F.IF.8b(11) 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.F.IF.8c(11) 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 = 91.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay.F.IF.9(all) Compare properties of two functions using a variety of representations (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, a quantity increasing exponentially eventually exceeds a quantity increasing linearly.
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