Standards Map

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

Domain - Building Functions

Cluster - Build new functions from existing functions.

[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.

Resources:


  • Exponential function
    A function of the form y = a •bx where a > 0 and either 0 < b < 1 or b > 1. The variables do not have to be x and y. For example, A = 3.2 • (1.02)t is an exponential function.
  • Linear function
    A function with an equation of the form y = mx + b, where m and b are constants
  • Model
    A mathematical representation (e.g., number, graph, matrix, equation(s), geometric figure) for real-world or mathematical objects, properties, actions, or relationships.

Predecessor Standards:

  • 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.A-SSE.A.1
    Interpret expressions that represent a quantity in terms of its context.*
  • MI.A-SSE.A.1.a
    Interpret parts of an expression, such as terms, factors, and coefficients.
  • MI.A-SSE.A.1.b
    Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r)n as the product of P and a factor not depending on P.
  • MI.F-IF.C.7.e
    Graph exponential functions, showing intercepts and end behavior.*
  • 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.F-LE.A.2
    Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (including reading these from a table).*
  • MI.F-LE.B.5
    Interpret the parameters in a linear function or exponential function (of the form f(x) = bx + k) in terms of a context.*
  • 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.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-TF.B.5
    Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.*
  • PC.F-TF.A.3
    (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π-x, π + x, and 2π - x in terms of their values for x, where x is any real number.
  • AQR.F-TF.A.3
    (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π-x, π + x, and 2π - x in terms of their values for x, where x is any real number.