Mathematics | Course : Model Mathematics I (Integrated Pathway)
Domain - Interpreting Functions
Cluster - Understand the concept of a function and use function notation.
[MI.F-IF.A.2] - Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. For example, given a function representing a car loan, determine the balance of the loan at different points in time.
- Function
A mathematical relation for which each element of the domain corresponds to exactly one element of the range. - Function notation
A notation that describes a function. For a function ƒ, when x is a member of the domain, the symbol ƒ(x) denotes the corresponding member of the range (e.g., ƒ(x) = x + 3).
[MI.F-IF.A.1] -
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
[MI.F-IF.A.3] -
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 f(0) = f(1) = 1, f(n + 1) = f(n) + f(n - 1) for n = 1.
[MI.G-CO.A.2] -
Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
[MI.S-ID.B.6.a] -
Fit a linear function to the data and use the fitted function to solve problems in the context of the data. Use given functions fitted to data or choose a function suggested by the context. Emphasize linear and exponential models.*
[MII.F-BF.B.3] -
Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Include exponential, quadratic, and absolute value functions. Utilize technology to experiment with cases and illustrate an explanation of the effects on the graph.