MPA2 Review - Functions

MPA2 Review - Functions

Boyle

Objective:

Students will be able to identify, evaluate, operate with and compose functions.

Identifying Functions

Relations, Functions, Domain & Range

Multiple Choice

Which set of ordered pairs represents a function?

• {(5,3), (3,4), (6,3), (5,-2)}

• {(5,3), (16,4), (6,3), (14,-2)}

• {(-2,3), (3,4), (-2,7), (4,-2)}

Remember:

Functions do not have repeating x-values!

But they can have repeating y-values.

Multiple Select

Select which set of maps represents a function:

Remember:

A functions input always has to have the same output.

For example: If I plug in 4 for the function f(x)= x+2, I will get f(4)= 6...

I will never get another output number

Evaluate Functions

Plug input values in for x to get f(x) or y

Multiple Choice

Evaluate: f(x) = x² +3x -7 for f(3)

• 10

• 18

• 11

• 7

Multiple Choice

Evaluate: f(x) = 3x² -16 for f(-1)

• -13

• -19

• 14

• -7

Fill in the Blanks

F(x) = 4x³ + 9x -5

F(-2) =

Real World Problem

A rocket was launched from Wallops Island, VA on Sunday. Rockets are launched from all over the world. 

https://spaceflightnow.com/launch-schedule/

Open Ended

The height of the rocket in meters above the ground after t seconds is given by the function

h(t) = -4.9t2 + 280t

What will the height be in meters in 30 seconds?

Operations with Functions

Evaluate for each function with the given x value, find those outputs, perform given operation

Multiple Choice

Addition:

f(x) = 2x +11 and g(x)= -3x+10

(f + g)(3)=

• 5

• 19

• 18

• 6

Multiple Choice

Subtraction:

f(x) = 2x +11 and g(x)= -3x+10

(f - g)(2)=

• 11

• 15

• 6

• 19

Multiple Choice

Multiplication:

f(x) = 2x +11 and g(x)= -3x+10

(f * g)(-1)=

• 111

• 9

• 13

• 117

Multiple Choice

Division:

f(x) = 2x +11 and g(x)= -3x+16

(f /g)(1)=

• 14

• 1

• 13

• 3

Function Compositions

Evaluate one function given the x-value, then plug that value into the other (or next) function. Continue the process as needed.

Real World Problem: Function Compositions

Buying a T-shirt

Open Ended

I want to buy this 20 dollar shirt, and it is on sale at 15% off. How much does the shirt cost?

Open Ended

Now, you must calculate what the shirt will cost after sales tax (let's say it is 8%). What would be the total cost after tax?

Composite Function

If f(x) = The price of the shirt after the discount and g(x) = The price after sales tax

Then the function for the final cost of the shirt = g(f(x)).

Rules:

f(x)= 20(1-x) x being the discount → 15%

f(x)= 20(1-0.15)= $17

g(x)= (1.08)x x being the cost of the shirt after the discount

g(x)= (1.08)(17)= $18.36

Multiple Choice

f(x)= 2x²+5

g(x)= 4x+16

g(f(2))=

• 13

• 24

• 68

• 1,157

Multiple Choice

F(x) =x+3

g(x)= 2x-5

h(x)=x²

f(g(h(-1))=

• 0

• 2

• 5

• -3