Math 110 Test # 1

Friday July 8, 2005 Jacek Szmigielski
Math 110 Test # 1
Fill in the bubbles that correspond to the correct answers. No aids: no calculators,
closed book. You are not permitted to consult with your fellow students in any way.
Time: 60 minutes.
Question 1. The set of real numbers in both of the intervals [0, 2) and (−1, 0] is equal to
(A) (−1, 2) (B) (−∞, 2) (C) (−∞, ∞) (D) {0} (E) {2}
(F) [−1, 2) (G) (2, ∞) (H) [−1, 2]
Question 2. Let n be an integer greater than or equal to 1. The number of integers in the interval
) is
(−2n − 1 1
2 , n + 2
(A) 3n − 1 (B) 2n (C) 3n (D) n + 1 (E) 2n − 2
(F) 1 (G) 3n + 1 (H) 0
Question 3. The largest value of |x − y| for x, y ∈ [2, 6] is
(A) 4 (B) 2 (C) −4 (D) 0 (E) 6
(F) 8 (G) 10 (H) −1
Question 4. Solve the equality |5x + 1| = 2. The solution set is
(A) 3 7
5 , 5 (B) 1 3
5 , 5 (C) 2
5
(E) − 3 7
5 , 5 (F) −1, 1 (G) 2
3
Question 5. Solve the inequality |x + 3| > 2. The solution set is
, 3
5 (D) − 3 1
5 , 5
2 (H) − 1 1
5 , 5
, 3
(A) (−3, 2) (B) (−∞, −3) ∪ (−1, ∞) (C) (−∞, −3) ∪ (2, ∞) (D) (−∞, −5) ∪ (−1, ∞)
(E) (−3, 2] (F) [−3, 2) (G) (−∞, −5] ∪ [1, ∞) (H) (−∞, −5) ∪ (1, ∞)
Question 6. Solve the inequality x 2 + 2x + 1 < 0. The solution set is
(A) (−1, 1) (B) {−1} (C) (−∞, 1) (D) {±1}
(E) ∅ (F) [−1, 1] (G) (−∞, 1] ∪ [1, ∞) (H) {0}

Question 7. The set of x such that 0 < x < 2π and (1 + sin x)(x − 2) = 0 is
(A) {−2π} (B) {2, −π} (C) ∅ (D) {2, π} (E) {π}
(F) {2} (G) {2, π
3π
2 } (H) {2, 2 }
Question 8. The length of the longest side in the triangle with vertices (0, 2), (−3, −1) and (1, −2)
is
(A) √ 14 (B) √ 15 (C) √ 16 (D) √ 17 (E) √ 18
(F) √ 19 (G) √ 20 (H) √ 21
Question 9. The value of m for which the lines 2x + 5y = 44 and mx − 4y = 55 are perpendicular
is
(A) 2
2
5
5 (B) 10 (C) 44 (D)
(F) π (G) − 5
2 (H) −10
44 (E) 1.5
Question 10. The line going through the points (1.25, 2.9), (2.75, 5.9) has slope equal to
(A) 1.5 (B) 1.75 (C) −3 (D) 2.75 (E) 2
(F) 1.9 (G) −1.9 (H) 3
Question 11. The value of tan 5π
4 is
1 (A) 1 (B) √2
(C) − 1 √
2
1
1
(F) 2 (G) 2 (H) √3
Question 12. The value of tan x if cos x = − 1
3
(A) 1 √3
and π < x < 3π
2 is
(D) 0 (E) −1
(B) √ 3
3 (C) − √ 3 (D) 1 (E) −3
(F) π (G) √ 5 (H) √ 8
Question 13. If f(x) = 3x + 2 then the value of f(2) is
(A) 2 (B) 0 (C) −2x − 8 (D) 6x + 4 (E) 4
(F) 8 (G) −6 (H) 6
Question 14. If f(x) = 3x + 2 then the set of x such that f(x) > −1 is
(A) [ 1
1
1
3 , ∞) (B) ( 3 , ∞) (C) [1, ∞) (D) [− 3 , ∞) (E) (−∞, ∞)
, ∞) (G) [0, 1] (H) (−1, ∞)
(F) (− 1
3

y
1
1
y=f(x)
The remaining questions refer to the graph above, which is the graph of a function called f(x).
Question 15. The domain of f is
(A) ( 1
2 , 2) (B) (−1, 3] (C) [−1, 1] (D) (−2, 3) (E) (−∞, ∞)
, 2]
(F) [0, 1] (G) [−2, 3] (H) [ 1
2
Question 16. The value of f(2) is
(A) − 1
1
2 (B) −1 (C) 2 (D) 1 (E) 0
(F) −2 (G) 2 (H) does not exist
Question 17. The set of x such that f(x) ≥ 0 is
(A) [−2, − 1
1
1
2 ) ∪ [1, 3](B) (− 2 , 0) (C) [−2, − 2 ) ∪ (1, 3](D) [0, ∞) (E) (0, ∞)
, 1]
(F) (− 1
1
4 , 2] (G) (−∞, 0] (H) [− 2
Question 18. The range of f is
(A) (−∞, 0] (B) (−1, 2) (C) [−1, 2] (D) (−∞, ∞)
(E) [−2, 1] (F) [2, ∞) (G) (−∞, −1) ∪ (2, ∞) (H) (−∞, −1] ∪ [2, ∞)
Question 19. The set of x such that f(x) = 0 is
(A) {0, − 1
1
1
2 } (B) {1} (C) {− 2 1} (D) {0, 2
(F) ∅ (G) {0} (H) (∞, ∞)
Question 20. If f(x) = 1 and x < 1
2 then x is
x
1
, 1} (E) { 2 , 1}
(A) −2 (B) − 1
2 (C) 0, 1 (D) 3 (E) 0, 1, 3
(F) 0 (G) 0, − 1
2 (H) none
Question 21. On exactly one of the following sets it is true that f is increasing. Which one?
(A) [−2, 1] (B) [−2, 0] (C) [−1, 0] ∪ {2} (D) (−∞, ∞) (E) (0, ∞)
, 1} (H) (−∞, 0)
(F) ( 1
1
2 , 2) (G) { 2

Next 6 questions refer to the functions f(x) = √ x − 2 and g(x) = 3x − 2.
Question 22. The value of (f + g)(6) is
(A) 14 (B) 16 (C) 18 (D) 20 (E) 22
(F) 24 (G) 26 (H) 28
Question 23. The value of g ◦ f(11) is
(A) 7 (B) √ 31 − 2 (C) 0 (D) √ 33 − 2 (E) 25
(F) −13 (G) 10 (H) 22
Question 24. The value of x such that f ◦ g(x) = g ◦ f(x) + 2 is
(A) 7
11
7
1
3 (B) 3 (C) 12 (D) 3 (E) − 11
3
(F) 0 (G) − 7
12 (H) 13
Question 25. The domain of the function f
g is
(A) (−∞, − 2 2
2
) ∪ ( , ∞) (B) (−∞, ∞) (C) (−∞, −
3
(F) (−∞, − 2
3
3
] ∪ ( 2
3
, ∞) (G) ( 2
3
, ∞) (H) [2, ∞)
Question 26. The domain of the function f ◦ g is
3
2
2
) (D) [ 3 , ∞) (E) { 3 }
(A) [ 4
4
3 , ∞) (B) (∞, ∞) (C) (−∞, 3 ] (D) [0, ∞) (E) (0, ∞)
, ∞) (G) (−∞, 0) (H) (−∞, 0]
(F) ( 4
3
Question 27. The value of f −1 (4) is
(A) 14 (B) 16 (C) 18 (D) 20 (E) 22
(F) 24 (G) 1
2 (H) 1
√2
Question 28. The exact value of log9( 1
3 ) is
1
(A) 3 (B) 2 (C) −3 (D) −2 (E) 3
(F) − 1
1
3 (G) 2 (H) − 1
2
Question 29. The value of x for which 2 3x−2 = 5 is:
1 3
1 2
1
(A) log2 5 + 2 (B) 3 ln 5 − 2 (C) 3 ln 5 + 3 (D) 3 log2 1 (F) 3 log 2
1
1
5 2 + 3 (G) 2 (H) √5 log2 5 + 2
3
Question 30. The exact value of 5 3 log 5 2−log 5 4+log 2 2 is
2
2
5 + 3 (E) 3
(A) 14 (B) 10 (C) 3 (D) 5 (E) 25
(F) 2 (G) 1 (H) 5
2
Question 31. If the function f(x) = 232x then the inverse function f −1 (x) is:
(A)
(F)
log2 x + log3 x
log2 log3 x
(B)
(G)
log2(log3 x)
3x
(C)
(H)
2 log3(log2 x)
−
(D) −2 log3(log2 x) (E)
log3 log2 x
3
2 log2 x

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The following questions refer to the above figure. Graph A of the figure is the graph of a function
y = f(x), while the other graphs are graphs of y = a + bf(cx + d), for various values of a, b, c and d.
Question 32. Graph B is the graph of the function
¨
¨
¨
(A) f(x − 4) (B) 4f(x) (C) f(−x) (D) f(−x) − 4 (E) f(x − 4) + 4
(F) f(x + 4) (G) f(x) + 4 (H) f(4 − x)
Question 33. Graph C is the graph of the function
(A) f(x − 2) + 5 (B) f(x + 4) (C) 2f(x − 2) + 3 (D) 2f(x + 8) (E) 2f(x − 4)
x − 8) (G) f(x − 4) (H) f(2x − 4)
(F) f( 1
2
Question 34. Graph D is the graph of the function
(A) f(−x) (B) f(x − 4) (C) f(x + 4) + 4 (D) −f(x) (E) f(x + 4)
(F) f(x − 4) + 4 (G) f(x) + 4 (H) −f(−x) − 1
Question 35. Graph E is the graph of the function
(A) −f(x) (B) f(x − 4) (C) f(x + 4) + 4 (A) −f(x) (E) f(x + 4)
(F) f(x − 4) + 4 (G) f(x) + 4 (H) −f(−x) − 1
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Question 36. Graph F is the graph of the function
1
3
(A) 2f(x + 2) +
5
f(x − 2) +
(F) 1
2
1
2 (B) f(x + 2) − 4 (C) 2
1
3
2 (G) f(x) + 4 (H) 2f(x − 2) − 2
5
f(x + 2) + 2 (D) f(x − 2) + 4 (E) f(x − 2)