Composing functions
in this task, you will compose functions algebraically, determine how the commutative property relates to function composition, and compose functions represented in different ways.

question 1
let f(x) = x − 3 and g(x) = x2 + 2.

part a
find (f ◦ ).

part b
find (g ◦ ).

part c
is function composition commutative? justify your answer.

question 2
part a
question
drag each tile to the correct box.

use these functions to place the function compositions in order from least to greatest value.
f(x) = 2x2
g(x) = x − 2

tiles
(f ◦ )(g ◦ )(f ◦ g)(3.5)(g ◦ f)(3.5)(f ◦ g)(0)(g ◦ f)(0)

part b
drag the tiles to the correct boxes to complete the pairs. not all tiles will be used.

use these functions to perform each function composition.

f(x) = 2x3

g(x) = x − 2

tiles
-2a3 − 2
2a3 − 2
2(a − 2)3
2(-a − 2)3
(2a − 2)3
(-2a − 2)3
pairs
(f ◦ g)(a)
arrowboth
(g ◦ f)(a)
arrowboth
(f ◦ )
arrowboth
(g ◦ )
arrowboth

question 3
question
type the correct answer in each box. if necessary, use / for the fraction bar.

use these functions to evaluate each function composition.