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Mathematics > Course Model Algebra I (Traditional Pathway) > Building Functions
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Mathematics | Course : Model Algebra I (Traditional Pathway)

Domain - Building Functions

Cluster - Build new functions from existing functions.

[AI.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).
  • 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:

  • AI.A-REI.B.3
    Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
  • AI.A-REI.B.3.a
    Solve linear equations and inequalities in one variable involving absolute value.
  • AI.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 (range) of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
  • AI.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, quadratic, exponential, and absolute value functions. Utilize technology to experiment with cases and illustrate an explanation of the effects on the graph.
  • AII.A-REI.A.2
    Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
  • AII.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.*