Algebra and Trigonometry 6th Edition Blitzer Solutions Manual

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Full download http://goo.gl/r6CkZV Algebra and Trigonometry 6th Edition Blitzer Solutions Manual6th Edition, Algebra and Trigonometry, Blitzer, Solutions Manual
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  Chapter 2 Functions and Graphs Copyright © 2018 Pearson Education, Inc. 201  Section 2.1 Check Point Exercises 1.  The domain is the set of all first components: {0, 10, 20, 30, 42}. The range is the set of all second components: {9.1, 6.7, 10.7, 13.2, 21.7}. 2. a.  The relation is not a function since the two ordered pairs (5, 6) and (5, 8) have the same first component but different second components. b.  The relation is a function since no two ordered pairs have the same first component and different second components. 3. a.  2662  x y y x  + == −  For each value of  x  , there is one and only one value for  y , so the equation defines  y  as a function of  x  . b.   22222 111  x y y x  y x  + == −= ± −  Since there are values of  x   (all values between –1 and 1 exclusive) that give more than one value for  y  (for example, if  x   = 0, then 2 101  y  = ± − = ± ), the equation does not define  y  as a function of  x  . 4. a.   2 (5)(5)2(5)725(10)742  f   − = − − − += − − +=   b.   222 (4)(4)2(4)7816287615  f x x x  x x x  x x  + = + − + += + + − − += + +   c.   222 ()()2()7(2)727  f x x x  x x  x x  − = − − − += − − += + +   5.    x    ( ) 2  f x x  =   ( ) ,  x y  -2 –4 ( ) 2,4 − −  -1 –2 ( ) 1,2 − −  0 0 ( ) 0,0 1 2 ( ) 1,2 2 4 ( ) 2,4  x    ( ) 23 g x x  = −   ( ) ,  x y  -2 ( ) 2(2)3 27 g  − − = − = −   ( ) 2,7 − −  -1 ( ) 2(1)3 15 g  − − − = = −   ( ) 1,5 − −  0 ( ) 2(0)3 03 g  − = = −   ( ) 0,3 −  1 ( ) 2(1)3 11 g  − = = −   ( ) 1,1 −  2 ( ) 2(2)3 21 g  − = =   ( ) 2,1 The graph of g  is the graph of  f   shifted down 3 units. Algebra and Trigonometry 6th Edition Blitzer Solutions Manual Full Download: http://testbanklive.com/download/algebra-and-trigonometry-6th-edition-blitzer-solutions-manual/  Full download all chapters instantly please go to Solutions Manual, Test Bank site: TestBankLive.com  Chapter 2 Functions and Graphs   202 Copyright © 2018 Pearson Education, Inc. 6.  The graph (a) passes the vertical line test and is therefore is a function. The graph (b) fails the vertical line test and is therefore not a function. The graph (c) passes the vertical line test and is therefore is a function. The graph (d) fails the vertical line test and is therefore not a function. 7. a.  (5)400  f   =   b.  9  x   = , (9)100  f   =   c.  The minimum T cell count in the asymptomatic stage is approximately 425. 8. a.  domain:   { }  [ ] 21 or 2,1.  x x  − ≤ ≤ −   range:   { }  [ ] 03 or 0,3.  y y ≤ ≤   b.  domain:   { }  (  ] 21 or 2,1.  x x  − < ≤ −   range:   { }  [  ) 12 or 1,2.  y y − ≤ < −   c.  domain:   { }  [  ) 30 or 3,0.  x x  − ≤ < −   range:   { } 3,2,1.  y y  = − − −  Concept and Vocabulary Check 2.1 1.  relation; domain; range 2.  function 3.    f  ;  x    4.  true 5.  false 6.    x  ; 6  x  +   7.  ordered pairs 8.  more than once; function 9.  [0,3); domain 10.  [1,) ∞ ; range 11.  0; 0; zeros 12.  false Exercise Set 2.1 1. The relation is a function since no two ordered pairs have the same first component and different second components. The domain is {1, 3, 5} and the range is {2, 4, 5}. 2.  The relation is a function because no two ordered pairs have the same first component and different second components The domain is {4, 6, 8} and the range is {5, 7, 8}. 3.  The relation is not a function since the two ordered pairs (3, 4) and (3, 5) have the same first component but different second components (the same could be said for the ordered pairs (4, 4) and (4, 5)). The domain is {3, 4} and the range is {4, 5}. 4.  The relation is not a function since the two ordered pairs (5, 6) and (5, 7) have the same first component but different second components (the same could be said for the ordered pairs (6, 6) and (6, 7)). The domain is {5, 6} and the range is {6, 7}. 5.  The relation is a function because no two ordered pairs have the same first component and different second components The domain is {3, 4, 5, 7} and the range is {–2, 1, 9}. 6.  The relation is a function because no two ordered pairs have the same first component and different second components The domain is {–2, –1, 5, 10} and the range is {1, 4, 6}. 7. The relation is a function since there are no same first components with different second components. The domain is {–3, –2, –1, 0} and the range is {–3, –2, –1, 0}. 8.  The relation is a function since there are no ordered pairs that have the same first component but different second components. The domain is {–7, –5, –3, 0} and the range is {–7, –5, –3, 0}. 9. The relation is not a function since there are ordered pairs with the same first component and different second components. The domain is {1} and the range is {4, 5, 6}. 10.  The relation is a function since there are no two ordered pairs that have the same first component and different second components. The domain is {4, 5, 6} and the range is {1}.   Section 2.1  Basics of Functions and Their Graphs   Copyright © 2018 Pearson Education, Inc. 203  11.  1616  x y y x  + == −  Since only one value of  y  can be obtained for each value of  x  ,  y  is a function of  x  . 12.  2525  x y y x  + == −  Since only one value of  y  can be obtained for each value of  x,    y  is a function of  x.   13.   22 1616  x y y x  + == −  Since only one value of  y  can be obtained for each value of  x  ,  y  is a function of  x  . 14.  22 2525  x y y x  + == −  Since only one value of  y  can be obtained for each value of  x,    y  is a function of  x.   15.   22222 161616  x y y x  y x  + == −= ± −  If  x   = 0, 4.  y  = ±  Since two values,  y  = 4 and  y  = – 4, can be obtained for one value of  x  ,  y  is not a function of  x  . 16. 22222 252525If 0, 5.  x y y x  y x  x y + == −= ± −= = ±  Since two values,  y  = 5 and  y  = –5, can be obtained for one value of  x,    y  is not a function of  x.   17.   2  x y y x  == ±  If  x   = 1, 1.  y  = ±  Since two values,  y  = 1 and  y  = –1, can be obtained for  x   = 1,  y  is not a function of  x  . 18.  4242If 1, then 2.  x y y x x  x y == ± = ±= = ±  Since two values,  y  = 2 and  y  = –2, can be obtained for  x = 1  ,    y  is not a function of  x.   19.  4  y x  = +  Since only one value of  y  can be obtained for each value of  x  ,  y  is a function of  x  . 20. 4  y x  = − +  Since only one value of  y  can be obtained for each value of  x,    y  is a function of  x.   21.   333 888  x y y x  y x  + == −= −  Since only one value of  y  can be obtained for each value of  x  ,  y  is a function of  x  . 22.   333 272727  x y y x  y x  + == −= −  Since only one value of  y  can be obtained for each value of  x,    y  is a function of  x.   23. 21  xy y + =   ( ) 2112  y x  y x  + ==+   Since only one value of  y  can be obtained for each value of  x,    y  is a function of  x.  24. 51  xy y − =   ( ) 5115  y x  y x  − ==−   Since only one value of  y  can be obtained for each value of  x,    y  is a function of  x.  25. 2  x y − =   22  y x  y x  − = − += −   Since only one value of  y  can be obtained for each value of  x,    y  is a function of  x.  26. 5  x y − =   55  y x  y x  − = − += −   Since only one value of  y  can be obtained for each value of  x,    y  is a function of  x.    Chapter 2 Functions and Graphs   204 Copyright © 2018 Pearson Education, Inc. 27. a.    f  (6) = 4(6) + 5 = 29 b.    f  (  x   + 1) = 4(  x   + 1) + 5 = 4  x   + 9 c.    f  (–  x  ) = 4(–  x  ) + 5 = – 4  x   + 5 28. a.  f  (4) = 3(4) + 7 = 19 b.  f  (  x + 1) = 3(  x   + 1) + 7 = 3  x   + 10 c.    f  (–  x  ) = 3(–  x  ) + 7 = –3  x   + 7 29. a.   2 (1)(1)2(1)31232 g  − = − + − += − +=   b.   222 (5)(5)2(5)3102521031238 g x x x  x x x  x x  + = + + + += + + + + += + +   c.   22 ()()2()323 g x x x  x x  − = − + − += − +   30. a.   2 (1)(1)10(1)311038 g  − = − − − −= + −=   b. 222 (2)(2)10(82)34410203619 g x x  x x x  x x  + = + − + −= + + − − −= − −   c.   22 ()()10()3103 g x x x  x x  − = − − − −= + −   31. a.   42 (2)221164113 h  = − += − +=   b.   42 (1)(1)(1)11111 h  − = − − − += − +=   c.   4242 ()()()11 h x x x x x  − = − − − + = − +   d.   4242 (3)(3)(3)18191 h a a aa a = − += − +   32.   a.   3 (3)33125 h  = − + =   b. 3 (2)(2)(2)18215 h  − = − − − += − + += −   c.   33 ()()()11 h x x x x x  − = − − − + = − + +   d.   33 (3)(3)(3)12731 h a a aa a = − += − +   33. a.  (6)663033  f   − = − + + = + =   b.  (10)1063163437  f   = + += += +=   c. (6)6633  f x x x  − = − + + = +   34. a.  (16)2516696363  f   = − − = − = − = −   b.  (24)25(24)6496761  f   − = − − −= −= − =   c.  (252)25(252)626  f x x  x  − = − − −= −   35. a.   22 4(2)115(2)42  f   −= =   b.   22 4(2)115(2)4(2)  f   − −− = =−   c.   2222 4()141()()  x x  f x  x x  − − −− = =−   36. a. 33 4(2)133(2)82  f   += =   b. 33 4(2)13131(2)88(2)  f   − + −− = = =−−   c. 3333 4()141()()  x x  f x  x x  − + − +− = =− −   33 41or  x  x  −     Section 2.1  Basics of Functions and Their Graphs   Copyright © 2018 Pearson Education, Inc. 205  37.   a.  6(6)16  f   = =   b.  66(6)166  f   − −− = = = −−   c.   22222 ()1 r r  f r r r  = = =   38. a. 538(5)1538  f  += = =+   b. 5322(5)15322  f  − + −− = = = = −− + − −   c.  93(9)93  x  f x  x  − − +− − =− − +  61, if 61,if 66  x  x  x  x  − − < −  = =   − > −− −     39.    x    ( )  f x x  =   ( ) ,  x y   − 2 ( ) 22  f   − = −   ( ) 2,2 − −   − 1 ( ) 11  f   − = −   ( ) 1,1 − −  0 ( ) 00  f   =   ( ) 0,0 1 ( ) 1 1  f   =   ( ) 1,1 2 ( ) 22  f   =   ( ) 2,2  x    ( ) 3 g x x  = +   ( ) ,  x y   − 2 ( ) 2231 g  − = − + =   ( ) 2,1 −   − 1 ( ) 1132 g  − = − + =   ( ) 1,2 −  0 ( ) 0033 g  = + =   ( ) 0,3 1 ( ) 1134 g  = + =   ( ) 1,4 2 ( ) 2235 g  = + =   ( ) 2,5 The graph of g  is the graph of  f   shifted up 3 units. 40.    x    ( )  f x x  =   ( ) ,  x y   − 2 ( ) 22  f   − = −   ( ) 2,2 − −   − 1 ( ) 11  f   − = −   ( ) 1,1 − −  0 ( ) 00  f   =   ( ) 0,0 1 ( ) 1 1  f   =   ( ) 1,1 2 ( ) 22  f   =   ( ) 2,2  x    ( ) 4 g x x  = −   ( ) ,  x y   − 2 ( ) 2246 g  − = − − = −   ( ) 2,6 − −   − 1 ( ) 1145 g  − = − − = −   ( ) 1,5 − −  0 ( ) 0044 g  = − = −   ( ) 0,4 −  1 ( ) 1143 g  = − = −   ( ) 1,3 −  2 ( ) 2242 g  = − = −   ( ) 2,2 −  The graph of g  is the graph of  f   shifted down 4 units. 41.  x    ( ) 2  f x x  = −   ( ) ,  x y  –2 ( )  ( ) 22 24  f   − = −  − =   ( ) 2,4 −  –1 ( )  ( ) 12 12  f   − = −  − =   ( ) 1,2 −  0 ( )  ( ) 02 00  f   = −  =   ( ) 0,0 1 ( )  ( ) 12 12  f   = −  = −   ( ) 1,2 −  2 ( )  ( ) 22 24  f   = −  = −   ( ) 2,4 −    x ( ) 21 g x x  = − −   ( ) ,  x y  –2 ( )  ( ) 2213 2 g  − = − − = −   ( ) 2,3 −  –1 ( )  ( ) 1211 1 g  − = − − = −   ( ) 1,1 −  0 ( )  ( ) 0211 0 g  = − − = −   ( ) 0,1 −  1 ( )  ( ) 1213 1 g  = − − = −   ( ) 1,3 −  2 ( ) ( ) 22215 g  = − − = −   ( ) 2,5 −  
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