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Mathematics > Course Model Mathematics II (Integrated Pathway) > Building Functions
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Mathematics | Course : Model Mathematics II (Integrated Pathway)

Domain - Building Functions

Cluster - Build new functions from existing functions.

[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.

Resources:


  • Expression
    A mathematical phrase that combines operations, numbers, and/or variables (e.g., 32 ÷ a).
  • Inverse function
    A function obtained by expressing the dependent variable of one function as the independent variable of another; that is the inverse of y = f(x) is x = f –1(y).
  • Linear function
    A function with an equation of the form y = mx + b, where m and b are constants

Predecessor Standards:

No Predecessor Standards found.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • MI.A-REI.B.3
    Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
  • MI.A-REI.B.3.a
    Solve linear equations and inequalities in one variable involving absolute value.
  • 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-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 linear and exponential models. (Focus on vertical translations for exponential functions). Utilize technology to experiment with cases and illustrate an explanation of the effects on the graph.
  • MIII.A-REI.A.2
    Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
  • MIII.F-LE.A.4
    For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.*
  • PC.F-BF.B.4.b
    (+) Verify by composition that one function is the inverse of another.
  • PC.F-BF.B.5
    (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
  • PC.F-TF.B.6
    (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
  • PC.F-TF.B.7
    (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.*
  • AQR.F-TF.B.7
    (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.*