F.7.PC

F.7.PC

F.7.PC.1Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example: The Fibonacci sequence is defined recursively by (0) = (1) = 1, f(n + 1) = f(n) + (n − 1) for n ≥ 1.F.7.PC.2Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example: Calculate mortgage payments.F.7.PC.3(+) Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.F.7.PC.4For 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. Note: Key features may include but not limited to: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.F.7.PC.5Calculate and interpret the average rate of change of a function (presented algebraically or as a table) over a specified interval. Estimate the rate of change from a graph.F.7.PC.6Graph functions expressed algebraically and show key features of the graph, with and without technology.F.7.PC.7Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).F.7.PC.8Build functions to model real-world applications using algebraic operations on functions and composition, with and without appropriate technology (e.g., profit functions as well as volume and surface area, optimization subject to constraints)
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