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Math

Mississippi Math

Algebra II: Functions: Building Functions (F-BF)

Build a function that models a relationship between two quantities

F-BF.1

Write a function that describes a relationship between two quantities.

F-BF.1.a

Mostly covered
Determine an explicit expression or steps for calculation from a context.

F-BF.1.b

Fully covered
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.1.c

Mostly covered
Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.

F-BF.2

Fully covered
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

F-BF.3

Partially covered
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.4.a

Fully covered
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)=2x^3 or f(x) = (x+1)/(x-1) for x ≠ 1.

F-BF.4.b

Fully covered
Verify by composition that one function is the inverse of another.

F-BF.4.c

Fully covered
Read values of an inverse function from a graph or a table, given that the function has an inverse.

F-BF.4.d

Fully covered
Produce an invertible function from a non-invertible function by restricting the domain.