1. Determine the domain and range of the relation.
{(Callie, A), (Steve, D), (Aaron, C), (Elton, B), (Macy, C), (Avery, B)}
2. Determine the domain and range of the relation.
{(Bob, 1), ( Matt, 2), (Mary, 3), (Pam, 4)}
3. Evaluate the expression x3 – 2x2 – x + 9 for the indicated value of x.
(a) x = –3 (b) x = 3 (c) x = –1
4. True or False: The following relation is a function.
The number of miles driven each day for a five-day trip. Let an ordered pair be given in the form (day, miles).
5. True or False: The following relation is a function.
{(Jose, 10), (Luigi, 8), (Estella, 1), (Lars, 9)}
6. True or False: The following relation, given as a table of values, is a function.
x y
–5 –30
6 –27
–5 11
10 9
7. True or False: The following relation is a function.
The revenue for each of 5 days in one particular week is:
{( Monday, $1525), (Tuesday, $1150), (Wednesday, $1770), (Thursday, $1560), (Friday, $2165)}
10. Use the table to find P(30).
x P(x)
30 2500
35 3000
40 4000
50 3800
11. Use the table to find j(0).
x j(x)
-2 5
-1 0
0 4
1 7
13. Let f(x) = –3x + 1 and g(x) = –x2 – 2x + 9. Find (f + g)(x).
14. Let f(x) = –5x2 + 7x – 8 and g(x) = –12x + 4. Find (f – g)(x).
15. Let f(x) = x + 1 and g(x) = –x2 – x + 1. Find (f • g)(x).
16. Let f(x) = 6 and g(x) = 5x + 3. Find (f g)(x).
21. Let f(x) = x + 1 and g(x) = x2 – 1. Find (3).
22. Rewrite the function h(x) = 4x2 as a composite of functions f(x) = x2 and g(x) = 2x.
24. The total cost in hundreds of dollars of producing x items per hour in an 8-hour shift is given by the function C(x) = 6x. Suppose that the number of items produced per hour for an 8-hour period is a function of the time t after an 8-hour shift begins and is given by x(t) = –t2 + 7t + 8, . Write a function f(t) to represent the hourly cost in hundreds of dollars at time t.
25. The area A of a circle as a function of the radius r is given by A(r) = . Suppose that the radius of a circle increases as a function of time and is given by r(t) = 0.9t, where the radius r is length in meters and t is time in seconds. Find and interpret f(t) = (A ? r)(t).