MA19.PRE.27

Mathematics (2019) Grade(s): 09-12 - Precalculus

MA19.PRE.27
Compose functions. Extend to polynomial, trigonometric, radical, and rational functions.

Unpacked Content

Knowledge

Students know:

Techniques for expressing functional relationships (explicit expression, a recursive process, or steps for calculation) between two quantities.
Techniques to combine functions using arithmetic operations.
Techniques to compose functions using algebraic operations.
Notation for function composition.

Skills

Students are able to:

Accurately develop a model that shows the functional relationship between two quantities.
Accurately create a new function through arithmetic operations of other functions.
Accurately create a new function through composition of other functions.
When functions are combined to create a new function, present an argument to show how the function models the relationship between the quantities.

Understanding

Students understand that:

Relationships can be modeled by several methods (e.g., explicit expression or recursive process).
Arithmetic combinations and/or composition of functions may be used to improve the fit of a model.

Vocabulary

Explicit expression
Recursive process
Compose functions

COS Examples

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.

Aligned Learning Resources

Analyzing the Graphs of Functions