M408K Hm. 1 Solutions

M408K Hm. 1 Solutions - Mahon, Kevin Homework 1 Due: Sep 13...

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Unformatted text preview: Mahon, Kevin Homework 1 Due: Sep 13 2005, 3:00 am Inst: Edward Odell 1 This print-out should have 25 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Simplify the difference quotient f ( x + h )- f ( x ) h , ( h 6 = 0) , as much as possible when f ( x ) = 4 x 2 + 7 x- 16 . 1. 8 x + 7 2. 8 x- 7 + 4 h 3. 8 x + 7 + 4 h correct 4. 4 x- 7 + 4 h 5. 4 x + 7 + 4 h Explanation: Now f ( x + h ) = 4( x + h ) 2 + 7( x + h )- 16 = 4 x 2 + 8 xh + 7 x + 4 h 2 + 7 h- 16 , while f ( x ) = 4 x 2 + 7 x- 16 . Thus f ( x + h )- f ( x ) = 8 xh + 4 h 2 + 7 h. Consequently, f ( x + h )- f ( x ) h = 8 x + 7 + 4 h . 002 (part 1 of 2) 10 points There is a linear relationship T F = mT C + b between the temperature T F on the Fahren- heit scale and its equivalent T C on the Centi- grade scale. As the thermometers 32 212 100 Freezing Boiling Farenheit Centigrade show, water freezes at 32 F and boils at 212 F, whereas it freezes at 0 C and boils at 100 C. Determine the relationship between T c and T F 1. T C = 9 5 T F + 32 2. T F = 9 5 T C- 32 3. T F = 5 9 T C + 32 4. T F = 9 5 T C + 32 correct 5. T F = 5 9 T C- 32 Explanation: Since water freezes at 32 F and at 0 C, T C = 0 = T F = 32 in the linear equation T F = mT C + b , so b = 32. On the other hand, since water boils at 212 F and at 100 C, T C = 100 = T F = 212; i.e. , 212 = 100 m + 32, so m = 9 5 . Conse- quently, T F = 9 5 T C + 32 . Mahon, Kevin Homework 1 Due: Sep 13 2005, 3:00 am Inst: Edward Odell 2 003 (part 2 of 2) 10 points Convert- 35 2 C to its Fahrenheit equivalent. 1.- 35 2 C 1 2 F correct 2.- 35 2 C - 1 2 F 3.- 35 2 C - 5 2 F 4.- 35 2 C - 3 2 F 5.- 35 2 C 3 2 F Explanation: Substituting for T C =- 35 2 in T F = 9 5 T C + 32 , we see that- 35 2 C is equivalent to- 63 2 + 32 F. Hence- 35 2 C 1 2 F. 004 (part 1 of 1) 10 points Find the function g that results after the following transformations are applied in the order given to the graph of a function f : (1) stretch along y-axis by a factor 8; (2) reflect about the x-axis; (3) shift down 3 units; (4) reflect about the y-axis. 1. g ( x ) = 24- 8 f ( x ) 2. g ( x ) = 24 + 8 f (- x ) 3. g ( x ) = 8 f ( x )- 24 4. g ( x ) =- 3- 8 f (- x ) correct 5. g ( x ) = 24- 3 f (- x ) Explanation: Beginning with a function y = f ( x ), the four transformations change f ( x ) as follows: f ( x ) (1)- 8 f ( x ) (2)- - 8 f ( x ) (3)- - 3- 8 f ( x ) (4)- - 3- 8 f (- x ) . Consequently, g ( x ) =- 3- 8 f (- x ) ....
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This note was uploaded on 04/15/2008 for the course M 408k taught by Professor Schultz during the Fall '08 term at University of Texas at Austin.

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M408K Hm. 1 Solutions - Mahon, Kevin Homework 1 Due: Sep 13...

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