LAC 28:CXLII.3111. Interpreting Functions

A. Interpret functions that arise in applications in terms of the context. 1. 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. 2. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. 3. 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. B. Analyze functions using different representations. 1. Graph functions are expressed symbolically and show key features of the graph by hand in simple cases and by using technology for more complicated cases. a. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. b. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. c. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. 2. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. 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. b. Use the properties of exponents to interpret expressions for exponential functions and classify them as representing exponential growth or decay. 3. Compare properties of two functions each represented in a different way including algebraically, graphically, and numerically in tables, or by verbal descriptions.