LAC 28:CXLII.2515. Interpreting Functions

A. Understand the concept of a function and use function notation. 1. Recognize that sequences are functions whose domain is a subset of the integers. Relate arithmetic sequences to linear functions and geometric sequences to exponential functions. B. 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. Calculate and interpret the average rate of change of a function over a specified interval. Estimate the rate of change from a graph. C. 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. 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 properties of exponents to interpret expressions for exponential functions. 3. Compare properties of two functions each represented in a different way.