Building Functions

Determine an explicit expression, a recursive process, or steps for calculation from a context.

Combine standard function types using arithmetic operations

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.

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

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.

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.

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

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

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

Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Write a function that describes a relationship between two quantities.

Find inverse functions.