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3.7.1: Operating on Functions

Newspapers are printed on large sheets of paper that are folded in half to form the pages. Each side of each half is 1 page. For example, a newspaper that is made from 2 large sheets of paper has 8 pages. Use this information to answer the following questions.

1. If there are 10 sheets of paper in a particular newspaper issue, how many pages would there be?

2. What page numbers would appear in the center, or on the innermost sheet of this newspaper?

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3.7.1: Operating on Functions

3. What is the sum of the numbers in the center?

4. What is the sum of the page numbers that would appear on ANY one side of ANY sheet of the newspaper?

5. What is the sum of all the page numbers of the newspaper?

6. Write a rule in words or symbols that would give the sum of the pages for a newspaper with n sheets of paper.

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3.7.1: Operating on Functions

1. If there are 10 sheets of paper in a particular newspaper issue, how many pages would there be?

• Since each sheet of paper creates 4 pages when folded and printed on front and back, 10 sheets of paper would create 4 • 10 or 40 pages.

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3.7.1: Operating on Functions

2. What page numbers would appear in the center, or on the innermost sheet of this newspaper?

• Since half of 40 is 20 and the page numbering starts at 1, page numbers 20 and 21 would appear in the center.

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3.7.1: Operating on Functions

3. What is the sum of the numbers in the center?

• 20 + 21 = 41

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3.7.1: Operating on Functions

4. What is the sum of the page numbers that would appear on ANY one side of ANY sheet of the newspaper?

• Since n sheets of paper result in 4n pages, and the first page is numbered 1 instead of 0, the sum of the page numbers of any one side of one sheet is 4n + 1.

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3.7.1: Operating on Functions

5. What is the sum of all the page numbers of the newspaper?

• There are 10 sheets of paper and 20 sides. The total number of pages plus 1 is 41. Multiply this number by the number of sides.

• The sum of all of the page numbers is 20(41) or 820.

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3.7.1: Operating on Functions

6. Write a rule in words or symbols that would give the sum of the pages for a newspaper with n sheets of paper.

• 2n represents the number of sides of each sheet. Therefore, the sum of the pages of a newspaper with n sheets is 2n(4n + 1).

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3.7.1: Operating on Functions