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?
Here are some numbers in a list:
1, -3, -1/2, 3, 2, 1/4, 0.5
1
Question 1
1.
How many different numbers are in the list?
1
Question 2
2.
Make a new list containing the squares of all these numbers.
1
Question 3
3.
How many different numbers are in the new list?
1
Write 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.
1
Question 5
5.
A person is 5.5 feet tall. Do you know their height in inches?
1
1
1
1
1
1
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.”
1
Question 12
12.
A person is 5.5 feet tall. Do you know their height in inches?
1
Question 13
13.
A number is 5. Do you know its square?
1
1
1
1
1
Question 19
19.
Which input-output rules could describe the same function (if any)? Be prepared to explain your reasoning.
Question 4
4.
Explain why the two lists do not have the same number of different numbers.
Question 6
6.
A number is 5. Do you know its square?
Question 7
7.
The square of a number is 16. Do you know the number?
Question 8
8.
A square has a perimeter of 12 cm. Do you know its area?
Question 9
9.
A rectangle has an area of 16 cm^2. Do you know its length?
Question 10
10.
You are given a number. Do you know the number that is 1/5 as big?
Question 11
11.
You are given a number. Do you know its reciprocal?
Question 14
14.
The square of a number is 16. Do you know the number?
Question 15
15.
A square has a perimeter of 12 cm. Do you know its area?
Question 16
16.
A rectangle has an area of 16 cm^2. Do you know its length?
Question 17
17.
You are given a number. Do you know the number that is 1/5 as big?
Question 18
18.
You are given a number. Do you know its reciprocal?