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.

dhhghghghhrhbb it 5

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step-by-step explanation:

show us the graphs dude

step-by-step explanation:

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

i think it is c hope that