Arkansas: FM Math Standards

FM.3

• FM.3.BTAII.1 Create equations and inequalities in one variable and use them to solve problems. Note: Including but not limited to equations arising from: Linear functions; Quadratic functions; Exponential functions; Absolute value functions
• FM.3.BTAII.2 Create equations in two or more variables to represent relationships between quantities. Graph equations, in two variables, on a coordinate plane.
• FM.3.BTAII.3 Represent and interpret constraints by equations or inequalities, and by systems of equations and/or inequalities. Interpret solutions as viable or nonviable options in a modeling and/or real-world context.
• FM.3.BTAII.4 Rearrange literal equations using the properties of equality
• FM.3.BTAII.5 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.
• FM.3.BTAII.6 Relate the domain of a function to its graph. Relate the domain of a function 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.
• FM.3.BTAII.7 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.
• FM.3.BTAII.8 Graph functions expressed algebraically and show key features of the graph, with and without technology.
• FM.3.BTAII.9 Write expressions for functions in different but equivalent forms to reveal key features of the function.
• FM.3.BTAII.10 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
• FM.3.BTAII.11 Write a function that describes a relationship between two quantities.
• FM.3.BTAII.12 Identify the effect on the graph of replacing f(x) by f(x) + k,k f(x),f(kx),and f(x + k) for specific values of k (k, a constant both positive and negative). Find the value of k given the graphs of the transformed functions. Experiment with multiple transformations and illustrate an explanation of the effects on the graph with or without technology. Include recognizing even and odd functions from their graphs and algebraic representations for them.
• FM.3.BTAII.13 Solve an equation of the form y = f(x) for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = 2 x^2 or f(x) = (x + 1)/(x – 1) for x ≠ 1.
• FM.3.BTAII.14 Define appropriate quantities for the purpose of descriptive modeling (I.E., Use units appropriate to the problem being solved.)
• FM.3.BTAII.15 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities
• FM.3.BTAII.16 Solve linear inequalities and systems of linear inequalities in two variables by graphing.
• FM.3.BTAII.17 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers [e.g., the Fibonacci sequence is defined recursively by f(0) = f(1) = 1,f(n+1) = f(n) + f(n−1) for n ≥ 1]
• FM.3.BTAII.18 Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another
• FM.3.BTAII.19 Construct linear and exponential equations, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
• FM.3.BTAII.20 Use the properties of exponents to transform expressions for exponential functions For example: The expression 1.15t can be rewritten as (1.15^(1/12))^(12t) ≈ 1.012^(12t) to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.