FM.3.BTAII

FM.3.BTAII

FM.3.BTAII.1Create 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 functionsFM.3.BTAII.10Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).FM.3.BTAII.11Write a function that describes a relationship between two quantities.FM.3.BTAII.12Identify 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.13Solve 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.14Define appropriate quantities for the purpose of descriptive modeling (I.E., Use units appropriate to the problem being solved.)FM.3.BTAII.15Choose a level of accuracy appropriate to limitations on measurement when reporting quantitiesFM.3.BTAII.16Solve linear inequalities and systems of linear inequalities in two variables by graphing.FM.3.BTAII.17Recognize 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.18Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to anotherFM.3.BTAII.19Construct 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.2Create equations in two or more variables to represent relationships between quantities. Graph equations, in two variables, on a coordinate plane.FM.3.BTAII.20Use 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%.FM.3.BTAII.3Represent 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.4Rearrange literal equations using the properties of equalityFM.3.BTAII.5For 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.6Relate 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.7Calculate 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.8Graph functions expressed algebraically and show key features of the graph, with and without technology.FM.3.BTAII.9Write expressions for functions in different but equivalent forms to reveal key features of the function.
Goblins

1-on-1 AI tutoring aligned to FM.3.BTAII. Instant help for students, real-time insights for teachers.

Used in classrooms by 100,000+ students at Baltimore County, Plano ISD, Deer Valley USD, KIPP, and districts nationwide.

Free for teachers, forever →