Standards in Unit 3 Module 2:
MGSE9-12.F.IF.3- Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. (Generally, the scope of high school math defines this subset as the set of natural numbers 1,2,3,4...) By graphing or calculating terms, students should be able to show how the recursive sequence a1=7, an=an-1 +2; the sequence sn = 2(n- 1) + 7; and the function f(x) = 2x + 5 (when x is a natural number) all define the same sequence.
MGSE9-12.F.IF.4- Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decreasing, positive, or negative; relative maximums and minimums, and end behavior.
MGSE9-12.F.IF.5- 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.
MGSE9-12.F.IF.6- 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.
MGSE9-12.F.IF.7- Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.
MGSE9-12.F.IF.7a- Graph linear functions and show intercepts, maxima, and minima (as determined by the function or by context).
MGSE9-12.F.IF.7e- Graph exponential, showing intercepts and end behavior.
MGSE9-12.F.LE.1- Distinguish between situations that can be modeled with linear functions and with exponential functions.
MGSE9-12.F.LE.1a- Show that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. (This can be shown by algebraic proof, with a table showing differences, or by calculating average rates of change over equal intervals).
MGSE9-12.F.LE.1b- Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
MGSE9-12.F.LE.1c- Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.