Standards Map

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.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.

Resources:


  • Absolute value
    The absolute value of a real number is its (non-negative) distance from 0 on a number line.
  • 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
  • Quadratic function
    A function that can be represented by an equation of the form y = ax2 + bx + c, where a, b, and c are arbitrary, but fixed, numbers and a 0. The graph of this function is a parabola.

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:

  • AI.A-SSE.A.1
    Interpret expressions that represent a quantity in terms of its context.*
  • AI.A-SSE.A.1.a
    Interpret parts of an expression, such as terms, factors, and coefficients.
  • AI.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)t as the product of P and a factor not depending on P.
  • AI.F-IF.C.7.e
    Graph exponential functions showing intercepts and end behavior.*
  • AI.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.
  • 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.
  • AI.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).*
  • AI.F-LE.B.5
    Interpret the parameters in a linear or exponential function (of the form f(x) = bx + k) in terms of a context.*
  • AI.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 functions fitted to data or choose a function suggested by the context (emphasize linear and exponential models).
  • AII.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.