IM: 8.5.2: Introduction to Functions (Lesson) - Formative Staff | Library

Here are some numbers in a list:

1, -3, -1/2, 3, 2, 1/4, 0.5

1

How many different numbers are in the list?

1

Make a new list containing the squares of all these numbers.

1

How many different numbers are in the new list?

1

Explain why the two lists do not have the same number of different numbers.

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

A person is 5.5 feet tall. Do you know their height in inches?

1

A number is 5. Do you know its square?

1

The square of a number is 16. Do you know the number?

1

A square has a perimeter of 12 cm. Do you know its area?

1

A rectangle has an area of 16 cm^2. Do you know its length?

1

You are given a number. Do you know the number that is 1/5 as big?

1

You are given a number. Do you know its reciprocal?

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

A person is 5.5 feet tall. Do you know their height in inches?

1

A number is 5. Do you know its square?

1

The square of a number is 16. Do you know the number?

1

A square has a perimeter of 12 cm. Do you know its area?

1

A rectangle has an area of 16 cm^2. Do you know its length?

1

You are given a number. Do you know the number that is 1/5 as big?

1

You are given a number. Do you know its reciprocal?

1

Which input-output rules could describe the same function (if any)? Be prepared to explain your reasoning.

Are you ready for more?

1

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?