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

Domain - Interpreting Functions

Cluster - Analyze functions using different representations.

[MII.F-IF.C.8.b] - Use the properties of exponents to interpret expressions for exponential functions. Apply to financial situations such as Identifying appreciation/depreciation rate for the value of a house or car some time after its initial purchase: Vn=P(1+r)n. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, and y = (1.2) t /10, and classify them as representing exponential growth or decay.

Resources:


  • Exponent
    The number that indicates how many times the base is used as a factor, e.g., in 43 = 4 x 4 x 4 = 64, the exponent is 3, indicating that 4 is repeated as a factor three times.
  • 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.
  • Expression
    A mathematical phrase that combines operations, numbers, and/or variables (e.g., 32 ÷ a).
  • Percent rate of change
    A rate of change expressed as a percent. Example: if a population grows from 50 to 55 in a year, it grows by 5/50 = 10% per year.

Predecessor Standards:

  • 7.RP.A.3
    Use proportional relationships to solve multi-step ratio, rate, and percent problems. For example: simple interest, tax, price increases and discounts, gratuities and commissions, fees, percent increase and decrease, percent error.
  • 7.EE.A.1
    Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients. For example, 4x + 2 = 2(2x +1) and -3(x – 5/3) = -3x + 5.
  • 8.F.B.4
    Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • 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-LE.A.1.a
    Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.*
  • MII.N-RN.A.2
    Rewrite expressions involving radicals and rational exponents using the properties of exponents.
  • MII.A-SSE.B.3.c
    Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15t can be rewritten as (1.15 1/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.