Precalculus Student Solution Manual - Santa Ana …

1 Precalculus Student Solution Manual This Student solutions Manual is copyright 2015, Rice University. All Rights Reserved. Chapter 1 Try a. yes; b. yes. (Note: If two players had been tied for, say, 4th place, then the name would not have been a function of rank.) (d) g(5)= 1 m= (x)= (1)= 0 or x= a. yes, because each bank account has a single balance at any given time; b. no, because several bank account numbers mayhave the same balance; c. no, because the same output may correspond to more than one Yes, letter grade is a function of percent grade;b. No, it is not one-to-one. There are 100 different percent numbers we could get but only about five possible letter grades,so there cannot be only one percent number that corresponds to each letter No, because it does not pass the horizontal line { 5, 0, 5, 10, 15} ( , ) ,12 12, 52, values that are less than or equal to 2, or values that are greater than or equal to 1 and less than 3;b.

2 {x|x 2 or 1 x< 3};c.( , 2] [ 1, 3) domain =[1950,2002] range = [47,000,000,89,000,000] domain: ( , 2]; range: ( , 0] Solution $ $ years=$ years=$ per a+ 7 The local maximum appears to occur at ( 1, 28), and the local minimum occurs at (5, 80). The function is increasing on ( , 1) (5, ) and decreasing on ( 1, 5). fg (x)=f(x)g(x)=(x 1) x2 1 =x3 x2 x+ 1 f g (x)=f(x) g(x)=(x 1) x2 1 =x x2No, the functions are not the A gravitational force is still a force, soa(G(r))makes sense as the acceleration of a planet at a distancerfrom the Sun (due to gravity), butG(a(F))does not make (g(1)) =f(3) = 3 and g(f(4)) =g(1) = 3 This content is available for free at Solution (f(2)) =g(5) = a.))

3 8; b. [ 4, 0) (0, ) Possible answer:g(x)= 4 +x2h(x)=43 xf=h g( ) (t) =h(t) + 10 = + 30t+ The graphs off(x) and g(x) are shown below. The transformation is a horizontal shift. The function is shifted to the left by 2 (x)=1x- 1+ Solution (x)= f(x)x-2024g(x) 5 10 15 (x) =f( x)x-2024h(x) content is available for free at Solution Manual4 Notice: g(x) =f( x) looks the same asf(x). 4 6 8g(x)9 12 15 (x) = 3x- (x) =f 13x so using the square root function we get g(x) = |x 2| using the variablep for passing, |p 80| (x) = |x+ 2|+ 1 or x= (0) = 1, so the graph intersects the vertical axis at (0, 1).]

4 F(x) = 0 when x= 5 and x= 1 so the graph intersects the horizontal axis atStudent Solution Manual5 ( 5, 0) and (1, 0). x 1 or k 7; in interval notation, this would be ( , 1] [7, ) (2) = The domain of functionf 1 is ( , 2) and the range of functionf 1 is (1, ). (60) = 50. In 60 minutes, 50 miles are 1(60) = 70. To travel 60 miles, it will take 70 a. 3; b. 3y+ 1(x) =(2 x)2; domain of f: [0, ); domain of f 1: ( , 2] Exercises1. A relation is a set of ordered pairs. A function is a special kind of relation in whichno two ordered pairs have the same When a vertical line intersects the graph of a relation more than once, that indicates that for that input there is more than oneoutput.

5 At any particular input value, there can be only one output if the relation is to be a When a horizontal line intersects the graph of a function more than once, that indicates that for that output there is more thanone input. A function is one-to-one if each output corresponds to only one function9. function11. function13. function15. functionThis content is available for free at Solution Manual617. function19. function21. function23. function25. not a ( 3) = 11;f(2) = 1;f( a) = 2a 5; f(a) = 2a+ 5; f(a+h) = 2a+ 2h ( 3) = 5+ 5;f(2) = 5;f( a)= 2 +a+ 5; f(a)= 2 a 5; f(a+h)=2 a h+ ( 3) = 2;f(2) = 1 3 = 2;f( a) =| a 1| | a+ 1|; f(a) = |a 1| +|a+ 1|; f(a+h) = |a+h 1| |a+h+ 1| (x) g(a)x a=x+a+ 2, x a35.

6 ( 2) = 14; b. x= 337. (5) = 10; b. x= 1 orx= 439. (t) = 6 23t; ( 3) = 8; c. t= 641. not a function43. function45. function47. function49. function51. function53. (0) = 1; (x) = 3, x= 2 orx= 255. not a function so it is also not a one-to-one function57. one-to- one function59. function, but not one-to-one61. function63. function65. not a (x) = 1, x= ( 2) = 14;f( 1) = 11;f(0) = 8;f(1) = 5;f(2) = ( 2) = 4;f( 1) = ;f(0) = ;f(1) = ;f(2) = ( 2) =19;f( 1) =13;f(0) = 1;f(1) = 3;f(2) = 975. 20 Student Solution Manual777.[0, 100]79.[ , ]81.[ 1, 000, 000, 1,000,000]83.[0, 10]This content is available for free at Solution Manual885.

7 [ , ]87.[ 100, 100]89. a. g(5000) = 50;b. The number of cubic yards of dirt required for a garden of 100 square feet is a. The height of a rocket above ground after 1 second is 200 ft. b. the height of a rocket above ground after 2 seconds is The domain of a function depends upon what values of the independent variable make the function undefined or There is no restriction on x forf(x) =x3 because you can take the cube root of any real number. So the domain is all real numbers, ( , ). When dealing with the set of real numbers, you cannot take the square root of negative numbers. So x-values are restricted forf(x) =x to nonnegative numbers and the domain is [0, ).]

8 Student Solution Manual997. Graph each formula of the piecewise function over its corresponding domain. Use the same scale for the x-axis and y-axis for each graph. Indicate inclusive endpoints with a solid circle and exclusive endpointswith an open circle. Use an arrowto indicate or . Combine the graphs to find the graph of the piecewise ( , )101.( , 3]103.( , )105.( , )107.( , 12) ( 12, )109.( , 11) ( 11, 2) (2, )111.( , 3) ( 3, 5) (5, )113.( , 5)115.[6, )117.( , 9) ( 9, 9) (9, )119. domain: (2, 8], range [6, 8) 121. domain: [ 4, 4], range: [0, 2]123. domain: [ 5, 3), range: [0, 2]125.]

9 Domain: ( , 1], range: [0, ) 127. domain: 6, 16 16, 6 ; range: 6, 16 16, 6 129. domain: [ 3, ); range: [0, ) 131. domain: ( , )This content is available for free at Solution Manual10133. domain: ( , )135. domain: ( , )137. domain: ( , ) ( 3) = 1;f( 2) = 0;f( 1) = 0;f(0) = ( 1) = 4;f(0) = 6;f(2) = 20;f(4) = ( 1) = 5;f(0) = 3;f(2) = 3;f(4) = 16145. domain: ( , 1) (1, ) Solution Manual11window: [ , ]; range: [4, 100]window: [ , ]; range: [4, 100]149.[0, 8]151. Many answers. One function is f(x) =1x The domain is [0, 6]; it takes 6 seconds for the projectile to leave the ground and return to the ground154.]]

10 Yes, the average rate of change of all linear functions is The absolute maximum and minimum relate to the entire graph, whereas the local extremarelate only to a specific regionaround an open content is available for free at Solution (b+ 1)160. + 2h164. 113(13 +h) + 9h+ + 2h increasing on ( , ) (1, ), decreasing on ( , 1)174. increasing on ( , 1) (3, 4), decreasing on (1, 3) (4, )176. local maximum: ( 3, 60), local minimum: (3, 60) 178. absolute maximum at approximately (7, 150), absolute minimum at approximately ( , 220)180. a. 3000; b. 1250182. -4184. 27186. Local minimum at (3, 22), decreasing on ( , 3), increasing on (3, ) 190.