LAC 28:CXLII.2913. Interpreting Functions

A. Interpret quadratic 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 and end behavior. 2. 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. 3. Calculate and interpret the average rate of change of a quadratic function, presented symbolically or as a table, over a specified interval. Estimate the rate of change from a graph. B. Analyze linear, exponential, quadratic, absolute value, step, and piecewise-defined 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 (to include absolute value) 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 such as linear, quadratic, piecewise linear to include absolute value, or exponential, each represented in a different way, algebraically, graphically, numerically in tables, or by verbal descriptions.