#### Math - 2018-19

# MA.3 - Compositions of Functions and Inverses of Functions

MA.3The student willapplycompositions of functions and inverses of functions to practical situations andinvestigateandverifythe domain and range of resulting functions.

*Adopted: 2016*

### BIG IDEAS

### UNDERSTANDING THE STANDARD

*·
In
composition of functions, a function serves as input for another function.*

· The composition of functions f(x) and g(x) can be determined using the graphs of f(x) and g(x).

·
A graph of a
function and its inverse are symmetric about the line *y* = *x*.

*· (ƒ ◦ ƒ-1)( x) = (ƒ-1 ◦ ƒ)(x) = x*

### ESSENTIALS

**The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to**

·
MA.3_{1} **Determine**
the composition of functions algebraically and graphically.

·
MA.3_{2} **Determine**
the inverse of a function algebraically and graphically.

·
MA.3_{3} **Determine**
the domain and range of composite functions algebraically and graphically.

·
MA.3_{4} **Determine**
the domain and range of the inverse of a function algebraically and
graphically.

### KEY VOCABULARY

*Updated: May 29, 2018*