In problems 1 – 6, identify each relation as a function or not a function.
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1. |
2. |
3. |
4. |
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5. {(3 , 7)
, (6 , 1) , (9 ,
4) ,
(10 , 5) , (6 , 4)}
6. {(1 , 4)
, (2 , 5) , (3 ,
0) ,
(4 , 4) , (1 , 4)}
In problems 7 – 10, determine the domain and the range of
each of the graphed functions.
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7. |
8. |
9. |
10. |
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11. Given that
, calculate f(-4) and simplify as much as possible.
12. Given that
, calculate g(-8) and simplify as much as possible.
In problems 13 and
14, determine the domain of the
function.
13. 14. 
In problems 15 – 17,
let f(x)
= –x + 4 and 
.
15. Find (f
+ g)(x). 16. Find (f – g)(x). 17. Find 
.
In problems 18 – 20,
use any method to solve the equation. Write answers in simplified radical form
or as complex numbers, where possible.
18. 
19. 
20. (x –
1)(x + 1) = –5
21. The city water tank can be filled in 8 hours by Well A alone and in 12 hours by Well B alone. How long will it take the tank to fill if both wells are working?
22. Joe jogs 2.5 mph slower than Kathy jogs. In the time that it takes Joe to jog 30 miles, Kathy can jog 40 miles. Find the jogging speed of each person.
23. According
to the National Sporting Goods Association, the number of skateboarders of age x can be approximated by 
. Estimate the number
of sixty-year-old skateboarders.
24. The world
population, P(t), in billions, t years after 1980, can be approximated
by 
. Predict the world
population in the year 2020.
In problems 25 – 27, simplify the expression, and write the answer using positive exponent(s) only.
25. 
26. 
27. 
In problems 28 – 30, perform the indicated operation, and write the answer in simplified radical form.
28. 
29. 
30. 
In problems 31 – 33, perform the indicated operation, and write the answer in the form of a complex number.
31. (–11 + 6i)
– (9 – 2i) 32. (–11 + 6i)(9 – 2i) 33. 
In problems 34 – 36, solve the equation for x.
34. 
35. 
36. 
In problems 37 and 38, simplify as much as possible.
37. 
38. 
In problems 39 – 41, perform the indicated operation, and simplify as much as possible.
39. 
40. 
41. 
42. Let 
.
a. Calculate f(-1). b. Calculate f(0). c. Calculate f(3).
d.
Use the information in parts a,
b, and c to sketch the graph of .
In problems 43 – 46, solve for x.
43. 
44. 
45. 
46. 
47.
Calculate 
. 48. Calculate 
. 49. Calculate 
.
50.
Calculate 
. 51. Calculate 
. 52. Calculate 
.
53. Consider
the circle 
. 54. Consider the circle 
.
a. Determine the radius of the circle. a. Determine the radius of the circle.
b. Determine the center of the circle. b. Determine the center of the circle.
c. Use the results of parts a and b to sketch c. Use the results of parts a and b to sketch
the circle . the circle 
.
. .
.
55.Consider the parabola
. 56.Consider
the parabola
.
a. Determine the vertex. a. Determine the vertex.
b. Determine the y-intercept(s). b. Determine the y-intercept(s).
c. Determine the x-intercept(s). c. Determine the x-intercept(s).
d. Use the results of parts a, b, and c to d. Use the results of parts a, b, and c to
sketch the graph
of . sketch the graph of .
