Module 2 - Relations & Functions

Module 2 - Relations & Functions

MA.912.F.1.2 - Given a function represented in function notation, evaluate the function for an input in its domain. For a real world context, interpret the output

​WARM-UP & Review

Multiple Choice

Evaluate the Expression

$$8x\ +\ 3\ when\ x=2$$  

• 19

• 85

• 13

• -12

Multiple Choice

Evaluate the expression

2q + 3. When q = 5 

• 11
• 15
• 17
• 13

Multiple Choice

Evaluate the expression 2p - (p + 3) ÷ 3. When p = 6

• 1

• 3

• 5

• 9

Multiple Choice

Evaluate the expression 6 + 8f. When f = 4

• 8

• 18

• 38

• 56

Multiple Choice

Evaluate the expression x² - x. For x = 6

• 30

• 6

• 42

• 12

Multiple Choice

What letter is ordered pair (5,4)?

• M

• S

• P

• A

• B

Multiple Choice

What letter is ordered pair (-1,2)?

• G

• S

• P

• A

• B

Multiple Choice

What letter is ordered pair (6,-2)?

• M

• S

• P

• A

• B

Objective(s) & Standard(s)

• Determine whether relations are functions

• Evaluate functions using function notation for given values

MA.912.F.1.2 - Given a function represented in function notation, evaluate the function for an input in its domain. For a real world context, interpret the output

Multiple Choice

Which choice also represents the relation shown in the sets below as correct ordered pairs?

• {(1,2),(2,4)}

• {(2,1),(4,2),(6,2)}

• {(1,2),(2,4),(2,6)}

• {(2,2),(2,4),(2,6)}

Complete your notes

Multiple Choice

The first number in an ordered pair is...

• the larger number.

• the origin.

• the x-coordinate.

• the y-coordinate.

Multiple Choice

All of the x values of a relation are called what?

• Domain
• Range
• Relation
• Function

Multiple Choice

All of the y values of a relation are called what?

• Domain
• Range
• Relation
• Function

Multiple Choice

What is the domain of the mapping?

• {2, 3, 8}
• { (-4, 3), (1, 8), (3, 2), (7, 3) }
• {-4, 1, 3, 7}
• {-4, 1, 2, 3, 7, 8}

Multiple Choice

What is the range of the table?

• {-4, 0, 1, 3}
• {-2, 0, 2, 3}
• {-4, -2, 0, 1, 2, 3}
• { (0, 0), (2, -4), (3, 3), (-2, 1) }

Multiple Choice

State the range of the relation.

{ (3, -2) , (4, -3), (5, -4), (6, 0) }

• (3, -2, 4, -3)

• (-2, -3, -4, 0)

• {-4, -3, -2, 0 }

• { 3, 4, 5, 6 }

Multiple Choice

Is the relation a function? Why.

• Yes, because the x-value 11 has two y-values pair with it.
• Yes, because each x-value has only one y-value paired with it.
• No, because the x-value 11 has two y-values pair with it.
• No, because each x-value has only one y-value paired with it.

Multiple Choice

Is this mapping a function or not a function? 

• Function
• Not a Function 

Multiple Choice

Is this table a function or not a function? 

• Function
• Not a Function

Multiple Choice

Is this set of ordered pairs a function or not a function? 

• Function
• Not a Function 

Multiple Choice

Which set of values is a function?

• (9,5) (10,5) (9,-5) (10,-5)
• (3,4) (4,-3) (7,4) (3, 8)
• (6,-5) (7, -3) (8, -1) (9, 1)
• (2, -2) (5, 9) (5, -7) (1, 4)

Multiple Choice

Which ordered pair could you add to the following list of points to create a function?  (3, 5) (4, 9) (2, 5) 

• (3, 7)
• (4, 1) 
• (1, 9)
• (2, 6)

Complete your notes

Multiple Choice

Is this a function? Explain.

• Yes; it passes the horizontal line test.
• No; it is not a straight line.
• Yes; it passes the vertical line test.
• No; it does not pass the vertical line test

Multiple Choice

Is the relation a function?

• Function
• Not a Function

Multiple Choice

Is y a function of x?

• function

• not a function

Multiple Choice

What is the definition of function?

• Has inputs and outputs
• Every input has only ONE output
• Inputs have different outputs every time
• x-values and y-values

Open Ended

Do you think the graph below is or is not a function. Explain why you believe your answer is correct.

Complete your notes

Multiple Choice

Let 𝑓(𝑥)=𝑥−7. Find the value of 𝑓(2).

• 5

• -7

• 7

• -5

Multiple Choice

What is f(6) for the function f(x)=3x-8

• -8

• 10

• -144

• answer not here

Multiple Choice

What is  $$f\left(0\right)$$   for the function $$f\left(x\right)=2x+3$$  

• 2x

• -3

• 3

• 10

Multiple Choice

$f\left(x\right)=5x-12$ What is $f\left(-4\right)$

• -32

• -3

• -12

• 3

Multiple Choice

$f\left(x\right)=5x-12$ What is $f\left(-4\right)$

• -32

• -3

• -12

• 3

Complete your notes

Multiple Choice

For what value of x does f(x) = -2?

• 0
• -5
• 3
• -3

Multiple Choice

What is the value of f(-5)?

• -2

• 2

• 4

• 0

Multiple Choice

What is F(-8)?

• 2

• -4

• -2

• 0

Multiple Choice

Find h(-1)

• -3

• 15

• 4

• 3

Multiple Choice

Find h(0)

• 2

• 15

• 4

• 3

Multiple Choice

Find x if h(x) = 23

• -1

• -2

• 23

• 17

Multiple Choice

Find x if h(x) = 0

• 2

• 15

• 3

• 4

Multiple Choice

Given the following ordered pairs, find g(3).

g(x): {(0, 5), (3, 4), (5, 3)}

• 1

• 0

• 4

• 5

Multiple Choice

Given the following ordered pairs, find x if g(x) = 5

g(x): {(0, 5), (3, 4), (5, 3)}

• 3

• 0

• 4

• 5

Fill in the Blanks

Let $f\left(x\right)\ =\ 3x-5$  . Find f(-3)

Multiple Choice

For the function, $$f\left(x\right)=3x-5$$  . Find $$f\left(-2\right)+f\left(6\right)$$  

• 4

• 2

• -4

• 8

Multiple Choice

What is f(−4) +8 for the function f?

f(x) = 2x + 3

• -5

• 4

• 3

• -2

Multiple Choice

If f(x) = -4x - 5 and
g(x) = 3 - x,
what is g(-4) + f(1)?

• 7
• -2
• -9
• -10

Multiple Choice

Identify the function rule that best represents the following statement:
The total cost (C) for kilograms of beef (k) if each kilogram costs ​$2.55

• C = 2.55k
• C = 2.55 + k
• C = 2.55 - k
• C = 2.55k + 2.55

Multiple Choice

Identify the function rule that best represents the following statement:
A bottle rocket is being launched from the roof of an 80 meter tall building. If the rocket travels straight up at a rate of 22 m/s, what is the total height of the rocket as a function of time?

• H = 108x
• H = 80 - 22x
• H = 80 + 22x
• H = 80x + 22

Multiple Choice

A plumber charges a service fee of $40 plus $25 per hour for labor.
(A) Write a function rule for the total cost of hiring the plumber for a job that takes x hours.
(B) How much would it cost to hire the plumber for a job that takes 4 hours?

• (A) y = 40 + 25x
  (B) $140
• (A) y = 40x + 25
  (B) $185
• (A) y = 40 + 25x 
  (B) $185
• (A) y = 40x + 25 
  (B) $140