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Mathematics > Course Model Mathematics I (Integrated Pathway) > Interpreting Functions
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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.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).

Resources:


  • Function
    A mathematical relation for which each element of the domain corresponds to exactly one element of the range.

Predecessor Standards:

  • 8.F.A.1
    Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [Note: Function notation is not required in grade 8.]
  • 8.F.A.3
    Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • 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.
  • MI.F-IF.B.4
    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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior.*
  • MI.F-IF.B.5
    Relate the domain of a function to its graph and, where applicable, 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.
  • MI.F-IF.C.7.a
    Graph linear functions and show intercepts.*
  • MI.F-IF.C.7.e
    Graph exponential functions, showing intercepts and end behavior.*
  • MI.F-IF.C.9
    Translate among different representations of functions: (algebraically, graphically, numerically in tables, or by verbal descriptions). Compare properties of two functions each represented in a different way. For example, given a graph of one exponential function and an algebraic expression for another, say which has the larger y-intercept.
  • MI.F-BF.A.1
    Write linear and exponential functions that describe a relationship between two quantities.*
  • MI.F-BF.A.1.a
    Determine an explicit expression, a recursive process, or steps for calculation from a context.*
  • MI.F-BF.A.1.b
    Combine standard function types using arithmetic operations.* For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
  • 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).
  • MII.F-IF.C.7.b
    Graph piecewise-defined functions, including step functions and absolute value functions.*
  • MII.F-BF.B.4
    Find inverse functions algebraically and graphically.
  • MII.F-BF.B.4.a
    Solve an equation of the form f(x) = c for a linear function f that has an inverse and write an expression for the inverse.
  • MIII.F-IF.C.7.c
    Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.*
  • MIII.F-TF.A.2
    Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
  • PC.F-IF.C.7.d
    (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.*
  • PC.F-BF.B.4
    Find inverse functions.
  • PC.F-BF.B.4.b
    (+) Verify by composition that one function is the inverse of another.
  • PC.F-BF.B.4.c
    (+) Read values of an inverse function from a graph or a table, given that the function has an inverse.
  • PC.F-BF.B.4.d
    (+) Produce an invertible function from a non-invertible function by restricting the domain.