Key to 1113 Exam #1 Review
1.a) input
b) output
c) Domain: {-4,-1,0,1,3,7,12}; Range: {5,7,3,15,8,9,10}
d) Every input is paired with exactly one output.
e) f (4)  5 ; f (3)  8 .
2. a) -2
b) 8
f) x  0
c) 14
3. a) Yes; every input gives exactly one output. You can solve it for y and graph it and it
passes the vertical line test.
b) No; some inputs give 2 outputs. Example: Let x = 0. Then y could be 1 or -1.
4. a) No; it fails the vertical line test.
b) Yes; it passes the vertical line test.
5. a) 1980-1998
b) 1998
c) In 1985, the number of movie admissions was 1.06 billion.
d) The number of movie admissions increased over this time period.
e) Every input is paired with exactly one output.
6. a) f (W )  0.105W  5.80
b) f (1000)  110.8 ; If a customer uses 1000 kwh, their bill will be $110.80.
c) $163.30
7. a) x  4
8.
b) [3, )
c) (, )
d) (, )
The window [-10, 10] × [-50, 50] gives a more complete graph, shown below.
9.
x
f (x )
-8
-5
24
43
240 108 1616 5340
10. a) 1985  5; 1990  10; 2005  25
b) f (20)  30,007 ; In the year 2000, the cost of prizes and expenses was $30,007 million.
c) xmin  0; xmax  29
11. a)
b) 1950-2000
c) It increased.
d) In 1960, it was 105.35;
In 1998, it was 262.062;
12. a) -2
b)
1
2
13. a) 1.834
c) The lines are perpendicular.
b) The per capita tax burden grew by 1.834 hundred dollars per year.
14. a) The value decreased by $20,000 per year. (-20000 is the slope.)
b) y  20,000 x  700,000
c) The y-intercept is 700,000. This means the initial value of the building is $700,000.
d) The x-intercept is 35. This means that after 35 years, the value of the building is $0.
15. a) Yes
b) The marginal cost is $0.73 per ball.
16. a) y  6
e) y  13 x  1
b) x  5
f) y  6 x  9
c) $6130
c) y  83 x  2
d) y  52 x  75
17. C  0.20t  3.95
18. P  699t  181; The membership in 2002 was 4375.
19. a) $18,500
c) V  2312.5t  23,500
b) $2312.50 per year
20. y  125 x  3375
19
9
21. a) x  6
b) x 
23. 122°F
24. In the year 2012.
22. a)
zQ  n
p
3
b) x 
5m  y
3 y
25. Approximately 1982.