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STANDARDS

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US-AR

Math

Arkansas Math

Pre-Calculus: Functions

Students will be able to find the inverse of functions and use composition of functions to prove that two functions are inverses.

F.6.PC.1

Not covered
Write a function that describes a relationship between two quantities.
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F.6.PC.2

Not covered
Find inverse functions.
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F.6.PC.3

Fully covered
Understand the inverse relationship between exponents and logarithms. Use the inverse relationship between exponents and logarithms to solve problems.

Students will be able to interpret different types of functions and their key characteristics including polynomial, exponential, logarithmic, power, trigonometric, rational, and other types of functions.

F.7.PC.1

Mostly covered
Recognize 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.2

Fully covered
Derive 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

Fully covered
(+) 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.
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F.7.PC.4

Partially covered
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. 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.5

Fully covered
Calculate 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.6

Not covered
Graph functions expressed algebraically and show key features of the graph, with and without technology.
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F.7.PC.7

Fully covered
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

F.7.PC.8

Fully covered
Build 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)