Calculus Concepts An

Calculus Concepts An Informal Approach to the Mathematics of Change, 5e Torre, Kenelly, Reed, Carpenter, Harris, Biggers (Solutions Manual All Chapter)

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Chapter 1 Ingredients of Change: Functions and Limits

Section 1.1 Functions —Four Representations (pages 8–12)

• A scatter-plot is a graphical. representation.
• Input is shown along the horizontal axis. Input is the number of years since 9/1/2000. , and the

units of measure are years..Output is shown along the vertical axis. Output is the performance of an investment. measured in dollars..

• The relation is a function. because only one performance amount is possible at any given time.

d.

• A table of data is a numerical. representation.
• Input is shown in the left column. Input is the military rank. and is unit-less..

Output is shown in the right column. Output is the basic monthly pay of a member of the military with a specific rank. measured in dollars..

• The relation is a function. because only one basic salary level is associated with each rank.

d.

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• 5e Calculus Concepts; LaTorre, et al.

Complete Solutions

©2012 Cengage Learning. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

• The statement is a verbal. representation.
• Input is the fraction of certain relatives who have had thyroid cancer.. The fraction used as input

is unit-less..Output is the chance of developing thyroid cancer. measured in percentage points..

• The relation is a function. because a specific percentage risk is associated with each fraction.

d.

• The statement is a verbal. representation.
• Input is the title of a book and is unit-less .

Output is the price on Amazon.com measured in dollars .c, d. The relation is not a function because the same title may sell for different prices.

• A formula is an algebraic representation.
• The input variable is n. Input is the number of correctly spelled words., and units of measure are

words..The output of the formula is ()gn. Output is a raw score which is unit-less..

• The relation is a function because a certain number of words spelled correctly results in only

one raw score.d.

• A scatter-plot is a graphical representation.
• The input is shown along the horizontal axis. Input is the number of years since 2000 and is

measured in years. .The output is shown along the vertical axis. Output is iPod sales. measured in thousand iPods.. 3 / 4

1.1 Functions—Four Representations 3 Complete Solutions

©2012 Cengage Learning. All rights reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

• The relation is a function because only one level of sales can correspond to any given year.

d.

(The variables used in the input/output diagram may vary because no variables were specified in the statement of the activity.)

• A table of a data is a numerical representation.
• The input is shown in the left column. Input is the diameter of the raw loaf , and the units of

measure are inches .The output is shown in the right column. Output is baking time measured in minutes .c, d.The relation is not a function because baking time for a given diameter can vary by 10- to 15- minutes.

• A formula is an algebraic representation.
• Input is the x-coordinate with a value between –6 and 6 . The input is unit-less .

Output is a y-coordinate on the circle . The output description is unit-less .c, d. The relation is not a function because each x-coordinate between –6 and 6 on the circle corresponds to two y -coordinates. Only the x-coordinates – 6 and 6 have a unique y-coordinate of 0.

• A statement is a verbal representation.
• Input is the calendar year , and the units of measure are years .

Output is the pre-season poll ranking and is unit-less .

• The relation is a function because there is only one ranking for each team in the Sports

Illustrated pre-season poll.d.

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