LAC 28:CXLII.2113. Interpreting Functions

A. Understand the concept of a function and use function notation. 1. Understand that a function from one set to another set 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). 2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. B. Interpret functions that arise in applications in terms of the context. 1. For linear, piecewise linear, quadratic, and exponential functions that model a relationship between two quantities: a. Interpret key features of graphs and tables in terms of the quantities, and b. Sketch graphs showing key features given a verbal description of the relationship. c. Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior. 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 linear, quadratic, piecewise linear, and exponential function over a specified interval. Estimate the rate of change from a graph. C. Analyze functions using different representations. 1. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima. b. Graph piecewise linear and exponential functions. 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. 3. Compare properties of two functions each represented in a different way.