Math 083
Practice Final Exam Solutions

1) This relation is a function because it passes the vertical line test.

2) This relation is not a function because it fails the vertical line test.

3) This relation is a function because it passes the vertical line test.

4) This relation is not a function because it fails the vertical line test.

5) The relation is not a function because the x-value 6 is paired with more than one y-value. (6,1), (6,4)

6) The relation is a function because the x-value is paired with exactly one y-value.

7) Domain:  All real numbers                Range:  All real numbers

8) Domain: -3 ≤ x ≤ 3                          Range:  0 ≤ y ≤ 3

9) Domain:  All real numbers                Range:  y ≤ 1

10) Domain:  x ≥- 4                             Range:  y ≤ -1

11)

12)

13)

14)                  

15)
 

16)

17) 

18)                                           

19)

20)

21)

22)

       Kathy’s rate is 10 miles per hour.  Joe’s rate is 7.5 miles per hour.

23)                                                                  24) 
                 
 
           

25)                                           26)                                                       27)
                                                                       

28)                                           29)                                                  30)

31)       (–11 + 6i) – (9 – 2i)                 32) (–11 + 6i)(9 – 2i)           
                        -20+8i                                 -99 + 22i + 54i - 12i^2
                                                                       -99 + 76i -12(-1)
                                                                              -87 + 76i
33)
           
34)                                                                   35)
                                 

36) 
           

37)                                           38) 
                        
39)                                                                               40)  

41)
           

42) 
Let

a.                                             b.                                 c. 

d.

43)

44)                                       

45)

46)

47) = 6                       48)   = 3                     49)    = 2

50)    = -2                 51)                      52)   

53)                                                                               54)
                                             

a. r=4                                                                         a.  r=

b. (-2, 1)                                                                    b. (0, -3)

55)                                                          56)