[F.BF.] Building Functions

Objectives

Build a function that models a relationship between two quantities. [For F.BF.1, 2, linear, exponential, and quadratic]

• • F.BF.1 Write a function that describes a relationship between two quantities.

    • F.BF.1a Determine an explicit expression, a recursive process, or steps for calculation from a context.

    • F.BF.1b 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.

• F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Build new functions from existing functions. [Linear, exponential, quadratic, and absolute value; for F.BF.4a, linear only]

• • F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

  • F.BF.4 Find inverse functions.

    • F.BF.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = 2 x³ or f(x) = (x+1)/(x-1) for x ≠ 1.