IM Alg1.4.2 Lesson: Function Notation
Here are the graphs of some situations you saw before. Each graph represents the distance of a dog from a post as a function of time since the dog owner left to purchase something from a store. Distance is measured in feet and time is measured in seconds.
| Day 1 | Day 2 | Day 3 |
 |  |  |
Use the given graphs to answer these questions about each of the three days:
Consider the statement, “The dog was 2 feet away from the post after 80 seconds.” Do you agree with the statement?
What was the distance of the dog from the post 100 seconds after the owner left?
Let’s name the functions that relate the dog’s distance from the post and the time since its owner left: function f for Day 1, function g for Day 2, function h for Day 3. The input of each function is time in seconds, t. Complete the table.
Describe what represents in this context.
Describe what represents in this context.
Describe what represents in this context.
The equation can be interpreted to mean: “On Day 2, 120 seconds after the dog owner left, the dog was 4 feet from the post.” What does the equation mean in this situation?
What does the equation mean in this situation?
What does the equation mean in this situation?
Rule B takes a person’s name as its input, and gives their birthday as the output. Complete the table with three more examples of input-output pairs.
Rule P takes a date as its input and gives a person with that birthday as the output. Complete the table with three more examples of input-output pairs.
If you use your name as the input to , how many outputs are possible? Explain how you know.
If you use your birthday as the input to , how many outputs are possible? Explain how you know.
Only one of the two relationships is a function. The other is not a function. Which one is which? Explain how you know.
For the relationship that is a function, write two input-output pairs from the table using function notation.
Write a rule that describes these input-output pairs:
Here are some input-output pairs with the same inputs but different outputs:
What rule could define function ?