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.
Compare There is an increasing linear pattern. Check yourself: :
Your answer may vary, but here are some samples.
Input: Skai Jackson;
Output: 2020
Input: Keke Palmer;
Output: 2010
Your second input-output pair example:
Compare your answers:
Your answer may vary, but here are some samples.
Input: Jeremy Pena;
Output: 2015
Input: Mike Trout;
Output: 2009
Your third input-output pair example:
Compare your answers:
Your answer may vary, but here are some samples.
Input: Bryce Young;
Output: 2020
Input: Patrick Mahomes;
Output: 2014
2. Complete the table for Rule P with three more examples of input-output pairs
Your first input-output pair example:
Compare your answer
Your answer may vary, but here are some samples.
Input: 2012;
Output: Ariana Grande
Input: 2012;
Output: Drake
Your second input-output pair example:
Compare your answers:
Your answer may vary, but here are some samples.
Input: 2020;
Output: Will Anderson, Jr.
Input: 2019;
Output: Kenyon Green
Input: 2015;
Output: Marisa Viggiano
Your third input-output pair example:
Compare your answers:
Your answer may vary, but here are some samples.
Input: 2018;
Output: Naomi Girma
Input: 2011;
Output: Lynn Williams
Input: 2018;
Output: Sophia Smith
3. If you use your own name as the input to G, explain how many outputs are possible and how you know.
Compare your answer:
Your answer may vary, but here is a sample.
One possible output. I can only graduate from high school once.
4. If you use your graduation date as the input to P, explain how many outputs are possible and how you know.
Compare your answer:
Your answer may vary, but here is a sample.
Many possible outputs. There are other people who will share the same graduation date as mine - especially my classmates who graduate with me.
5. Only one of these two relationships, G or P, is a function. The other is not a function. Which one is the function?
Compare your answers:
Rule G is a function and Rule P is not.
6. How do you know the relationship you chose is a function?
Compare your answers:
Your answer may vary, but here is a sample.
G only assigns one output to the input value.
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?
Compare your answers:
Your answer may vary, but here are some samples.
= 2008
= 2020
b. What is the second input-output pair example?
Compare your answers:
Your answer may vary, but here are some samples.
= 2015
= 2021
Are you ready for more?
Extending Your Thinking
1. Write a rule that describes these input-output pairs:
(ONE)
(TWO)
(THREE)
(FOUR)
What rule could define function ?
Compare your answers:
Function takes a word for its input and gives the number of letters in that word for its output.
2. Here are some input-output pairs with the same inputs but different outputs:
(ONE)
(TWO)
(THREE)
(FOUR)
What rule could define function ?
Compare your answers:
Function takes a word for its input and gives the number of vowels in that word as its output.
Self Check
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, , needed to cover a garden with an area of square feet is given by .
1. A garden with area 5000 requires 50 of dirt. Express this information in terms of the function .
Solution:
2. Explain the meaning of the statement .
Solution: The number of cubic yards of dirt required for a garden of 100 square feet is 1.
Example 2
Let be the number of ducks in a lake years after 1990. Explain the meaning of each statement:
1.
Solution: In 1995 (5 years after 1990), there were 30 ducks in the lake.
2.
Solution: In 2000 (10 years after 1990), there were 40 ducks in the lake.
Try it
Try It: Meanings in Functions
The amount of garbage, , produced by a city with population is given by . is measured in tons per week, and 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 .
Compare your answer:
2. Explain the meaning of the statement .
Compare your answer:
Five thousand people will produce 2 tons of garbage each week.