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6-8 Accelerated 7 Unit 6 Lesson 2

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Accelerated 6 •Accelerated 7

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Lesson 1 •Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18 Lesson 19 Lesson 20 Lesson 21 Lesson 22 Lesson 23

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Accelerated 6
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Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9

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Lesson 2
Lesson 3
Lesson 4
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Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
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Lesson 14
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IM K-5 Math
IM 6-8 Math
IM 9-12 Math

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Lesson 2

2.1 Warm-up 2.2 Activity 2.3 Activity 2.4 Activity Student Lesson Summary Glossary

Unit 6, Lesson 2

Introduction to Functions

Accelerated 7

2.1

Warm-up

Here are some numbers in a list:

1
-3
3
2
0.5

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.

2.2

Activity

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 bookshelf is 5.5 feet tall. Do you know its 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?

2.3

Activity

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 bookshelf is 5.5 feet tall. Do you know its 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?

2.4

Activity

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

Input-output rule diagram. Input, 7, right arrow, rule is, square it, right arrow, output, 49.

Input-output rule diagram. Input, 10, right arrow, rule is find the area given the side length, right arrow, output, 100.

Input-output rule diagram. Input, 10, right arrow, rule is, add 90, right arrow, output, 100.

Student Lesson Summary

Let’s say we have an input-output rule that gives exactly one output for each allowable input. Then we say the output depends on the input, or the output is a function of the input.

For example, the area of a square is a function of the side length because the area can be found from the side length by squaring it. So when the input is 10 cm, the output is 100 cm².

Function rule diagram, input, 10, right arrow, rule given is, find the area of a square given the side length, right arrow, output 100.

Sometimes we might have two different rules that describe the same function. As long as we always get the same single output from any given input, the rules describe the same function.

A function is a rule that has exactly 1 output for each possible input.

In the function , is the input and is the output. When is 5, has one value, 34.