MA19.PRE.35

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

MA19.PRE.35
Demonstrate that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

Unpacked Content

Knowledge

Students know:

Characteristics of an always increasing or always decreasing function.
When a function has an inverse that is also a function.

Skills

Students are able to:

Identify intervals where the function is increasing or decreasing.
Identify the domain of a function that will produce an inverse.
Produce different models of functions and their resulting inverse.

Understanding

Students understand that:

Due to the periodic nature of trig functions, domains have to be restricted in order to produce a one-to-one relationship.
While there are many different intervals that are always increasing or always decreasing, there are conventional choices for the restricted domain of the trig functions.

Vocabulary

Restricting the domain
Inverse functions

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