Test 1: Domain and range problems

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MQ6 TEST 1A  (answers below)                                                                                           Mr. G. Jaye

INSTRUCTIONS: 1. Express all answers in simplest form, SHOW ALL WORK, and box answers.
                              2. NO graphing calculators.   3. Use pen.

In 1 - 8, fill in all the answers. [6, 5, 4 off for first 3 wrong answers]
In #1- 3, fill in the three Pythagorean identities.
1. 2. 3.
In 4- 5, state the standard equation of the circle with the given center and radius.
4. C(h, k), radius r 5. C(0, 0), radius r
6. The standard formula for the distance between (x1, y1) and (x2, y2) is:
7. Given operation *; if x * y = y * x for all x, y, then * is a ???? operation.
8. By subjecting the graph of a relation to the ________________________________________ , one can     determine whether or not the relation is a function.

 

 

 

 

 

 

 

 

 

 

In 9- 13, fill in all the answers. [4, 3 off for first two wrong answers]
9. ry-axis(x, y) = 11. ry=- x(x, y) =
10. rx-axis(x, y) = 12. ry=x(x, y) =
13. R(x, y) =

 

 

 

 

 

In 14- 15, evaluate greatest integer function and fill in the answer. [2 each]
14. wpe40.gif (913 bytes) 15. wpe3F.gif (919 bytes)

 

 

 

In 16- 18, state whether or not the graph of the relation represents a function. (Y or N) [2 each]
16. Y or N:

wpe4.gif (1654 bytes)

         

17. Y or N:

wpe4.gif (1654 bytes)

 18. Y or N:

___

             ___

                             ___

                                            ___

 

 

 

 

 

 

 

 

In 19- 21, make rough sketch of graph of the relation and answer the accompanying questions. [8 each]
19. {(x, y) : x = p }

                                       

20. {(x, y): y = }

 

 21. {(x, y): x2 + y2 = 4}

 

 

 

 

 

wpe16.gif (1788 bytes)wpe17.gif (1783 bytes)wpe19.gif (1754 bytes)

19.

domain:

range:

 20.

domain:

range:

 21.

domain:

range:

In 22-30, SHOW WORK and box answers

22. Given the relation defined by 2x - 9y = 5 - 3xy:                                                               [6 each]
a. Find the domain algebraically.

 

 b.Find the range algebraically.

 

 

In 23- 27, find the domain of the relation.
23.  y =   1/(x + 5)                                                    [2] 26.  y =     Show work.                                  [5]
24.  y = 1/(x2 + 3x - 10)    Show work.                      [4] 27.                                                           [2]
25.  y =    Show work.               [8]

 

 

In 28 - 30, f(x) = and g(x) = x2 - 9.                                                                                [4, 4, 3]
28. Simplify  

 
29. Simplify 

 
30. The domain of  is:

 

 

ANSWERS: 1- 3. sin2q + cos2q = 1, tan2q + 1 = sec2q , and cot2q + 1 = csc2q   4. (x- h)2 + (y - k)2 = r2   5. x2 + y2 = r2
6. d = Ö [(x1- x2)2 + (y1- y2)2]     7. commutative    8. vertical line test     9. (- x,y)    10. (x,- y)     11. (- y,- x)   12. (y,x)
13. (- x,- y)    14. 3    15. - 3    16. Yes     17. No    18. Yes    19. {x = p }, {y Î R}    20. {x Î R}, {y = - Ö 2}
21. {- 2 £ x £ 2}, {- 2 £ y £ 2}    22. {x ¹ 3}, {y ¹ - 2/3}    23. {x ¹ - 5}    24. {x¹ - 5 and x¹ 2}  
25. {x £ - 8 or x ³ 6}    26. {- 3 £ x £ 3}    27. {x Î R}    28. Ö (x2 - 7)    29. x - 7     30. {x ³ - 2}

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