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Math 110 Practice Final Exam
1. Evaluate using the Piecewise Function:
๐(๐ฅ) = {โ3๐ฅ2 + 4๐ฅ โ 7 ๐ฅ โค โ5
5 โ5 < ๐ฅ โค 3|2๐ฅ โ 1| ๐ฅ > 3
a. ๐(2) = โ5 b. ๐(โ5) = 5
c. ๐(โ6) = 13 d. ๐(8) = 15
2. Given the Piecewise Function, Identify an open point of the graph.
๐(๐ฅ) = {2๐ฅ โ 12 ๐ฅ < โ2
๐ฅ + 4 โ2 โค ๐ฅ < 2โ6๐ฅ + 3 ๐ฅ โฅ 2
a. (โ2, โ2) b. (2, โ9)
c. (โ2, 16) d. (2, 6)
3. Find the new function given the set of equations: (๐ + 2๐)(๐ฅ)
๐(๐ฅ) = โ๐ฅ + 1 ๐(๐ฅ) = ๐ฅ2 + 1 โ(๐ฅ) = (๐ฅ + 1)2
a. ๐ฅ2 + 2 b. ๐ฅ2 โ ๐ฅ + 2
c. ๐ฅ2 โ 2๐ฅ + 3 d. ๐ฅ + 2
4. Find the Difference Quotient of the function: ๐ท๐ =๐(๐ฅ+โ)โ๐(๐ฅ)
โ
๐(๐ฅ) = โ5๐ฅ2 + 2
a. โ10โ b. โ10๐ฅ โ 5โ
c. โ5๐ฅ d. โ10๐ฅโ โ 5โ2
5. Use the given Table of Values to identify the correct Evaluation.
๐ฅ ๐(๐ฅ) ๐(๐ฅ) 1 3 8 3 1 9 8 9 1 9 8 3
a. (๐ โ ๐)(8) = 1 b. (๐ โ ๐)(9) = 3
c. (๐ โ ๐)(3) = 8 d. (๐ โ ๐)(9) = 9
6. Find the Composite function given the set of equations: (โ โ ๐)(๐ฅ)
๐(๐ฅ) = 3๐ฅ โ 4 ๐(๐ฅ) = 2๐ฅ2 โ 5 โ(๐ฅ) = 3(๐ฅ โ 1)2
a. 27๐ฅ2 โ 75 b. 27๐ฅ2 โ 90๐ฅ + 75
c. 18๐ฅ2 โ 17 d. 18๐ฅ2 โ 27๐ฅ + 45
7. Given the Graph, identify the correct evaluation:
a. (๐ โ ๐)(4) = 4 b. (๐ โ ๐)(4) = 4
c. (๐ โ ๐)(4) = 4 d. (๐ โ ๐)(4) = 4
8. Given the table of data, determine if the table can represent a One-to-One Function.
๐ฅ (Semester)
๐ฆ (Percent Passing)
F2012 48
S2013 55
F2013 52
S2014 46
F2014 51
a. No, ๐ฅ repeats b. Yes, ๐ฅ & ๐ฆ are unique
c. No, ๐ฆ repeats d. Yes, ๐ฅ & ๐ฆ both repeat
9. Consider the One-to-One function, Identify the correct statement about itโs inverse.
๐น(๐ฅ) = {(2,1), (3,2), (4,3), (5,4), (1,7)}
a. ๐โ1(2) = 3 b. ๐โ1(1) = 0
c. ๐โ1(4) = 7 d. ๐โ1(2) = 1
10. Consider the One-to-One graph of ๐(๐ฅ), Identify the correct evaluation for its inverse.
a. ๐โ1(โ1) = 2 b. ๐โ1(0) = โ1
c. ๐โ1(1) = 0 d. ๐โ1(โ3) = 4
11. Solve the Rational Equation: 4
๐ฅโ1+
7
๐ฅ+2=
3๐ฅโ7
(๐ฅโ1)(๐ฅ+2)
a. ๐ฅ = 2 b. ๐ฅ = โ1
c. ๐ฅ = 1 d. ๐๐ ๐๐๐๐ข๐ก๐๐๐
12. Find the Vertical Asymptotes: ๐(๐ฅ) =(๐ฅ+6)(๐ฅโ2)
(๐ฅโ3)(๐ฅ+4)
a. โ6 ๐๐๐ 2 b. 6 ๐๐๐ โ 2
c. โ3 ๐๐๐ 4 d. 3 ๐๐๐ โ 4
13. Identify the Domain: ๐(๐ฅ) =(๐ฅโ2)(๐ฅ+2)
(๐ฅโ2)(๐ฅโ1)
a. (โโ, โ2) โช (โ2, โ1) โช (โ1, โ) b. (โโ, 1) โช (1, 2) โช (2, โ)
c. (โโ, โ1) โช (โ1, โ) d. (โโ, โ2) โช (โ1, โ)
14. Which Rational Function has 2 Holes and 1 Vertical Asymptote?
a. ๐(๐ฅ) =(๐ฅ+3)(๐ฅโ1)(๐ฅ+1)
(๐ฅโ1)(๐ฅ+3)(๐ฅ+2) b. ๐(๐ฅ) =
(๐ฅ+2)(๐ฅโ7)(๐ฅ+3)
(๐ฅ+2)(๐ฅโ5)(๐ฅโ1)
c. ๐(๐ฅ) =(๐ฅโ2)(๐ฅ+1)(๐ฅ+5)
(๐ฅโ5)(๐ฅ+2) d. ๐(๐ฅ) =
(๐ฅ+5)(๐ฅโ3)(๐ฅ+1)
(๐ฅโ3)(๐ฅ+1)
15. Find the x-intercept values: ๐(๐ฅ) =๐ฅ2โ5๐ฅ+6
๐ฅ2โ4๐ฅโ5
a. โ3 ๐๐๐ โ 2 b. โ5 ๐๐๐ 1
c. โ1 ๐๐๐ 5 d. 2 ๐๐๐ 3
16. Find the y-intercept value: ๐(๐ฅ) =๐ฅ2+4
๐ฅโ2
a. โ2 b. 2
c. โ1 d. 1
2
17. Find the equation of the Horizontal Asymptote: ๐(๐ฅ) =3๐ฅ2+4๐ฅโ9
2๐ฅ3โ2๐ฅ2+5๐ฅโ1
a. ๐ฆ =3
2 b. ๐ฆ = 1
c. ๐ฆ = 0 d. ๐๐ ๐ป๐๐๐๐ง๐๐๐ก๐๐ ๐ด๐ ๐ฆ๐๐๐ก๐๐ก๐
18. Find the equation of the Oblique Asymptote: ๐(๐ฅ) =โ3๐ฅ3+๐ฅ2+2๐ฅโ6
๐ฅ2โ2๐ฅ+1
a. ๐ฆ = โ3๐ฅ โ 5 b. ๐ฆ = โ3๐ฅ + 7
c. ๐ฆ = 3๐ฅ โ 7 d. ๐๐ ๐๐๐๐๐๐ข๐ ๐ด๐ ๐ฆ๐๐๐ก๐๐ก๐
19. Identify the equation based on the graph:
a. ๐(๐ฅ) =(๐ฅ+1)(๐ฅโ7)(๐ฅ+2)
(๐ฅ+1)(๐ฅโ3) b. ๐(๐ฅ) =
(๐ฅโ1)(๐ฅ+7)(๐ฅ+2)
(๐ฅ+2)(๐ฅโ3)
c. ๐(๐ฅ) =(๐ฅโ1)(๐ฅโ7)(๐ฅโ2)
(๐ฅโ2)(๐ฅ+3) d. ๐(๐ฅ) =
(๐ฅ+1)(๐ฅโ7)(๐ฅ+2)
(๐ฅ+2)(๐ฅโ3)
20. Solve: ๐ฅ + 3 = โ14๐ฅ โ 6
a. โ3 ๐๐๐ โ 5 b. 3 ๐๐๐ 5
c. 3 d. ๐๐ ๐๐๐๐ข๐ก๐๐๐
21. Solve: |2๐ฅ โ 9| = 7
a. 1 & 8 b. 8 & โ 8
c. 1 & โ 1 d. โ1 & โ 8
22. Solve:
4|2๐ฅ โ 9| + 7 = 3
a. 4 & 5 b. 4 & โ 5
c. โ4 & โ 5 d. ๐๐ ๐๐๐๐ข๐ก๐๐๐
23. George has $5000 to invest in an account which compounds weekly at 3.8%. If he needs
$7250, how long will he need to leave his money invested? ๐ด = ๐ (1 +๐
๐)
๐๐ก ๐๐ ๐ด = ๐๐๐๐ก
a. 508.6 ๐ฆ๐๐๐๐ b. 9.7 ๐ฆ๐๐๐๐
c. 39.3 ๐ฆ๐๐๐๐ d. 17.5 ๐ฆ๐๐๐๐
24. The bank currently offers monthly interest at 5.4%, and George has $1200 to invest. How much
money will be in his account at the end of 6 years? ๐ด = ๐ (1 +๐
๐)
๐๐ก ๐๐ ๐ด = ๐๐๐๐ก
a. $1658 b. $1578
c. $1868 d. $1388
25. Solve:
log2(3๐ฅ + 25) + 4 = 8
a. 3 b. 0
c. โ3 d. ๐๐ ๐๐๐๐ข๐ก๐๐๐
26. Solve:
log(๐ฅ โ 7) + log(2๐ฅ + 3) = log (19)
a. โ3
2 ๐๐๐ 7 b. โ
5
2 ๐๐๐ 8
c. 7 d. 8
27. Given the Hydronium concentration, find the correct ๐๐ป of the substance.
๐๐ป = โ log[๐ป3๐+]
๐บ๐๐ฃ๐๐ [๐ป3๐+] = 3.7 ร 10โ4.83
a. 3.74 b. 4.83
c. 4.26 d. 5.68
28. A sound has a decibel level of 132. If it takes 5 machines to produce this loudness, find the
intensity of 1 machine.
๐ท = 10 โ log (5 โ ๐ผ
10โ12)
๐๐๐ก๐๐๐: 5 times the intensity is because we needed 5 machines to produce the loudness.
a. 3.1698 b. 15.8489
c. 1.58 ร 1013 d. 12.6990
29. An organism in a polluted water sample is recognized as active. Measurement #1 showed 187
organisms as active. 3 hours later, Measurement #2 showed 123 organisms as active. Find the
rate of decay for this population in this polluted environment.
๐ฆ = ๐๐๐๐ก
a. โ0.2193 b. โ0.5207
c. โ0.1396 d. โ0.6578
30. We want a colony to double in 36 months. What rate of growth should we hope to have?
๐ฆ = ๐๐๐๐ก
a. 0.1980 b. 0.1792
c. 0.0167 d. 0.0193
31. Identify the graph which shows the correct intersection of the lines.
{3๐ฅ โ 2๐ฆ = 52๐ฅ + 3๐ฆ = 7
a.
b.
c.
d.
32. Find the point of intersection for the given system of linear equations.
{3๐ฅ โ 4๐ฆ = 1
2๐ฅ + 3๐ฆ = 12
a. (โ1, โ1) b. (5, โ1)
c. (6, 0) d. (3, 2)
33. Identify the system of nonlinear equations which creates the graph.
a. {3๐ฅ2 + 2๐ฆ2 = 5
๐ฅ2 โ 3๐ฆ2 = 3 b. {
3๐ฅ2 โ 2๐ฆ2 = 5
๐ฅ2 + 3๐ฆ2 = 3
c. {3๐ฅ2 โ 2๐ฆ = 5
๐ฅ + 3๐ฆ2 = 3 d. {
3๐ฅ2 โ 2๐ฆ2 = โ5
๐ฅ2 โ 3๐ฆ2 = 3
34. Solve the nonlinear system of equations. Find all real points of intersection.
{๐ฅ2 + ๐ฆ2 = 12
โ๐ฅ2 + ๐ฆ = 0
a. (โ3, 3), (โโ3, 3) b. (3, โ4), (โ3, โ4)
c. (3, โ3), (3, โโ3), (โ4, 2), (4, 2) d. (โ3, 3), (โโ3, 3), (2, โ4), (โ2, 4)
35. Write the Augmented matrix as a system of equations.
[3 1 โ2 โฎ 71 โ1 โ3 โฎ 52 2 0 โฎ โ3
]
a. {3๐ฅ2 + ๐ฅ โ 2 = 7๐ฅ2 โ ๐ฅ โ 3 = 52๐ฅ2 + 2๐ฅ = โ3
b. {
3๐ฅ + ๐ฆ โ 2๐ง = 7๐ฅ โ ๐ฆ โ 3๐ง = 5
2๐ฅ + 2๐ฆ + ๐ง = โ3
c. {
3๐ฅ + ๐ฆ โ 2๐ง = 7๐ค๐ฅ โ ๐ฆ โ 3๐ง = 5๐ค2๐ฅ + 2๐ฆ = โ3๐ค
d. {
3๐ฅ + ๐ฆ โ 2๐ง = 7๐ฅ โ ๐ฆ โ 3๐ง = 52๐ฅ + 2๐ฆ = โ3
36. Solve the system of equations.
{
8๐ฅ + 2๐ฆ โ 5๐ง = โ13๐ฅ + 2๐ฆ + 3๐ง = โ4โ5๐ฅ + 4๐ฆ + ๐ง = 8
a. (1, 1, โ1) b. (โ1, 1, 1)
c. (โ1, 1, โ1) d. (1, โ1, 1)
37. Identify the type of system:
{4๐ฅ + 1๐ฆ = 5
8๐ฅ + 2๐ฆ = 10
a. Dependent b. Inverse
c. Consistent d. Inconsistent
38. Given the reduced matrix, write the solution:
[1 0 1 โฎ 10 1 1 โฎ 00 0 0 โฎ 4
]
a. (1 โ ๐ง, โ๐ง, ๐ง) b. (1, 0, 4)
c. (1 โ ๐ง, โ๐ง, 4) d. ๐๐ ๐๐๐๐ข๐ก๐๐๐
39. Given the reduced matrix, write the solution:
[1 0 3 40 1 โ1 00 0 0 0
]
a. (โ3๐ง + 4, ๐ง, ๐ง) b. (4
3, 1, ๐ง)
c. (3๐ง, โ1๐ง, 4๐ง) d. (๐ง, ๐ง, ๐ง)
40. The table shown represents 3 peopleโs trips to the concession stand at a baseball game. Use the
information to determine the price of one hotdog.
Hotdogs Cokes Pretzels Total spent
Sally 4 6 2 $26.80
Bink 6 3 1 $22.80
Roana 2 4 8 $28.80
a. $1.88 b. $2.28
c. $2.15 d. $2.35
41. A volleyball team paid $5 for a pair of socks and $17 for a pair of shorts. Last year, the total bill
was $315. This year, they purchased the same number of socks and shorts, but the total was
$342. Socks are now $6 a pair and shorts are $18 a pair. How many pairs of shorts did the team
buy? (Hint: try to set up a table like the one above)
a. 12 b. 15
c. 21 d. 8
42. Identify the system of inequalities that creates the feasible region shown:
a. {
๐ฅ + 3๐ฆ โค 198๐ฅ + ๐ฆ โค 73
โ๐ฅ + 7๐ฆ โค โ16๐ฅ โฅ 2
b. {
โ๐ฅ โ 3๐ฆ โค 198๐ฅ + ๐ฆ โฅ 73
๐ฅ โ 7๐ฆ โค โ16๐ฅ โฅ 2
c. {
โ๐ฅ + 3๐ฆ โค 198๐ฅ + ๐ฆ โค 73
โ๐ฅ โ 7๐ฆ โค โ16๐ฅ โฅ 2
d. {
โ๐ฅ + 3๐ฆ โค 198๐ฅ + ๐ฆ โฅ 73
โ๐ฅ โ 7๐ฆ โฅ โ16๐ฅ โฅ 2
43. Use the optimizing function to Minimize the feasible region created by the system:
{๐ฆ โค 5๐ฅ โฅ 2
โ๐ฅ + ๐ฆ โฅ โ1
๐ง = 8๐ฅ โ 2๐ฆ
a. 22 b. 38
c. 14 d. 6
44. The matrix simplification is not possible because _____.
[1 5 42 9 7
] + [8 91 30 2
]
a. Adding inverse matrices is wrong and causes mass destruction of sanity.
b. Addition is only possible when both matrices are perfectly square.
c. The number of rows of the first matrix do not match the number columns of the second matrix.
d. Both matrices must be exactly the same size in order to add them together.
45. Simplify the Matrix Expression:
2 [3 41 โ1
] [32
]
a. [6 122 โ2
] b. [342
]
c. [24 12] d. Not Compatible
46. The inverse of this matrix is impossible to compute because ______.
[3 โ42 6
โ1 5]
a. All entries must be positive values. b. The matrix must be square.
c. This matrix is too big. d. All entries must be 0 ๐๐ 1 ๐๐ โ 1.
47. Compute the inverse of the matrix:
๐ด = [1 0 00 โ1 0
โ1 0 1]
a. [1 0 00 โ1 01 0 1
] b. [โ1 0 00 1 01 0 โ1
]
c. [1 0 00 โ1 01 0 โ1
] d. [1 0 00 1 0
โ1 0 โ1]
48. Given the matrix equation, solve for ๐: ๐ด๐ฅ = ๐
a. ๐ฅ = ๐/๐ด b. ๐ฅ = ๐ดโ1๐
c. ๐ฅ = ๐โ1๐ด d. ๐ฅ = ๐๐ดโ1
49. Given the matrix equation, solve for ๐:
๐ด = ๐๐ถ when ๐ด = [5 72 3
] ๐๐๐ ๐ถ = [2 31 1
]
a. [2 โ10 1
] b. [2 11 0
] c. [1 21 1
] d. [โ1 21 โ1
]
50. Write the system of equations as a Matrix Equation:
{5๐ฅ โ 3๐ฆ + 7๐ง = 12
๐ฅ โ ๐ฆ = 2๐ฆ + 8๐ง = 9
a. [5 โ3 7 121 โ1 0 20 1 8 9
] b. [5 โ3 71 โ1 00 1 8
] [๐ฅ๐ฆ๐ง
] = [1229
]
c. [๐ฅ๐ฆ๐ง
] = [5 โ3 71 โ1 00 1 8
] [1229
] d. [๐ฅ๐ฆ๐ง
] = [5 โ3 71 โ1 00 1 8
]
โ1
[1229
]
Answer Key:
1 D
2 D
3 C
4 B
5 C
6 B
7 C
8 B
9 A
10 D
11 B
12 D
13 B
14 A
15 D
16 A
17 C
18 A
19 D
20 B
21 A
22 D
23 B
24 A
25 C
26 D
27 C
28 A
29 C
30 D
31 C
32 D
33 B
34 A
35 D
36 C
37 A
38 D
39 A
40 D
41 B
42 C
43 D
44 D
45 B
46 B
47 A
48 B
49 B
50 B