IM 8.5.2 Lesson: Introduction to Functions
Here are some numbers in a list:
How many different numbers are in the list?
Make a new list containing the squares of all these numbers.
How many different numbers are in the new list?
Explain why the two lists do not have the same number of different numbers.
Say yes or no for each question. If yes, draw an input-output diagram. If no, give examples of two different outputs that are possible for the same input.
A person is 5.5 feet tall. Do you know their height in inches?
If yes, draw the diagram like so: "input -> rule -> output". If no, give examples of two different outputs that are possible for the same input.
A number is 5. Do you know its square?
If yes, draw the diagram like so: "input -> rule -> output". If no, give examples of two different outputs that are possible for the same input.
The square of a number is 16. Do you know the number?
If yes, draw the diagram like so: "input -> rule -> output". If no, give examples of two different outputs that are possible for the same input.
A square has a perimeter of 12 cm. Do you know its area?
If yes, draw the diagram like so: "input -> rule -> output". If no, give examples of two different outputs that are possible for the same input.
A rectangle has an area of 16 cm2. Do you know its length?
If yes, draw the diagram like so: "input -> rule -> output". If no, give examples of two different outputs that are possible for the same input.
You are given a number. Do you know the number that is as big?
If yes, draw the diagram like so: "input -> rule -> output". If no, give examples of two different outputs that are possible for the same input.
You are given a number. Do you know its reciprocal?
If yes, draw the diagram like so: "input -> rule -> output". If no, give examples of two different outputs that are possible for the same input.
Here are the questions from the previous activity.
For the ones you said yes to, write a statement like, “The height a rubber ball bounces to depends on the height it was dropped from” or “Bounce height is a function of drop height.” For all of the ones you said no to, write a statement like, “The day of the week does not determine the temperature that day” or “The temperature that day is not a function of the day of the week.” A person is 5.5 feet tall. Do you know their height in inches?
A number is 5. Do you know its square?
The square of a number is 16. Do you know the number?
A square has a perimeter of 12 cm. Do you know its area?
A rectangle has an area of 16 cm2. Do you know its length?
You are given a number. Do you know the number that is as big?
You are given a number. Do you know its reciprocal?
Which input-output rules could describe the same function (if any)?
Explain your reasoning.
The phrase “is a function of” gets used in non-mathematical speech as well as mathematical speech in sentences like, “The range of foods you like is a function of your upbringing.”
What is that sentence trying to convey? Is it the same use of the word “function” as the mathematical one?