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Algebra 1

4.2.3 Finding a Unique Output for Each Input

Algebra 14.2.3 Finding a Unique Output for Each Input

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Activity

Rule G takes a person's name as its input and gives their high school graduation date as the output.

Input Output

Taylor Swift

2008

Zendaya

2015

Storm Reid

2020

Johnny Orlando

2021

Rule P takes a high school graduation date and gives a person with that graduation date as the output.

Input Output

2020

Lil Tecca

2021

Olivia Rodrigo

2022

Forrest Wheeler

2023

Miles Brown

1. Complete the table for Rule G with three more examples of input-output pairs.

Your second input-output pair example:

Your third input-output pair example:

2. Complete the table for Rule P with three more examples of input-output pairs

Your second input-output pair example:

Your third input-output pair example:

3. If you use your own name as the input to G, explain how many outputs are possible and how you know.

4. If you use your graduation date as the input to P, explain how many outputs are possible and how you know.

5. Only one of these two relationships, G or P, is a function. The other is not a function. Which one is the function?

6. How do you know the relationship you chose is a function?

7. For the relationship that is a function, write two input-output pairs from the table using function notation.

a. What is the first input-output pair example?

b. What is the second input-output pair example?

Are you ready for more?

Extending Your Thinking

1. Write a rule that describes these input-output pairs:

F F (ONE) = 3 = 3

F F (TWO) = 3 = 3

F F (THREE) = 5 = 5

F F (FOUR) = 4 = 4

What rule could define function F F ?

2. Here are some input-output pairs with the same inputs but different outputs:

v v (ONE) = 2 = 2

v v (TWO) = 1 = 1

v v (THREE) = 2 = 2

v v (FOUR) = 2 = 2

What rule could define function v v ?

Self Check

Self Check

The price for pizzas, in dollars, is a function of the number of pizzas bought, n .

p ( 11 ) = 55

  1. Input: 11
    Output: 55
    55 pizzas cost $11
  2. Input: 55
    Output: 11
    55 pizzas cost $11
  3. Input: 11
    Output: 55
    11 pizzas cost $55
  4. Input: 55
    Output: 11
    11 pizzas cost $55

Additional Resources

Meanings in Functions

Review the following examples to help you gain a better understanding of meanings in functions.

Example 1

The number of cubic yards of dirt, D D , needed to cover a garden with an area of a a square feet is given by D = g ( a ) D = g ( a ) .

1. A garden with area 5000 f t 2 f t 2 requires 50 y d 3 y d 3 of dirt. Express this information in terms of the function g g .

2. Explain the meaning of the statement g ( 100 ) = 1 g ( 100 ) = 1 .

Example 2

Let f ( t ) f ( t ) be the number of ducks in a lake t t years after 1990. Explain the meaning of each statement:

1. f ( 5 ) = 30 f ( 5 ) = 30

2. f ( 10 ) = 40 f ( 10 ) = 40

Try it

Try It: Meanings in Functions

The amount of garbage, G G , produced by a city with population p p is given by G = f ( p ) G = f ( p ) . G G is measured in tons per week, and p p is measured in thousands of people.

1. The town of Tola has a population of 40,000 and produces 13 tons of garbage each week. Express this information in terms of the function f f .

2. Explain the meaning of the statement f ( 5 ) = 2 f ( 5 ) = 2 .

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