DEPARTMENT OF ENGINEERING EDUCATION
Computer Engineering Program
UM Visayan Campus, Visayan Village, Tagum City,
Davao del Norte, Philippines
Tel #: (084) 655 - 6074
CEE 200 – Math Plus Page | 1
DEPARTMENT OF ENGINEERING EDUCATION
Computer Engineering Program
UM Visayan Campus, Visayan Village, Tagum City,
Davao del Norte, Philippines
Tel #: (084) 655 - 6074
Dear Students,
Greetings and welcome to Plate #2 for CEE 200 – Math Plus. This assignment provides a thorough
review of Rational Expressions, Complex Numbers, Functions, and Graphs, serving as a preparatory
exercise for the upcoming 2nd Examination.
To ensure a careful and successful completion of this assignment, kindly adhere to the following
guidelines:
1. Paper and Writing Instrument:
• Use the template for your plates posted in Google Classroom.
• Utilize a black ball-point pen for your solutions.
2. Clarity and Presentation:
• Express your solutions clearly so I can understand them easily. Make sure they make sense
and flow well.
• When you get the final answer, put it in a special box for emphasis.
3. Numeric Precision:
• In instances involving long floating-point answers, exercise precision by limiting your
answer to 4 digits, following a standard of mathematical thoroughness.
Submission Procedure:
• Submit a hardcopy of your solution at the Engineering Computer Laboratory by February
19, 2024, no later than 11:59 am. Punctuality is paramount, as late submissions will incur
deduction of points.
Your commitment to these guidelines is greatly appreciated, contributing to the seamless evaluation of
your efforts. Thank you for your cooperation, and best wishes for a successful completion of Plate #2.
Sincerely,
Engr. Godofredo L. Jipus Jr
CEE 200 Instructor
CEE 200 – Math Plus Page | 2
DEPARTMENT OF ENGINEERING EDUCATION
Computer Engineering Program
UM Visayan Campus, Visayan Village, Tagum City,
Davao del Norte, Philippines
Tel #: (084) 655 - 6074
Section 2.1: Rational Expressions
For problems 1 – 3, reduce the following rational expression to lowest terms.
𝑥 2 −6𝑥−7
1.
𝑥 2 −10𝑥+21
𝑥 2 +6𝑥+9
2.
𝑥 2 −9
2𝑥 2 −𝑥−28
3. 20−𝑥−𝑥 2
For problems 4 – 6, perform the indicated operations and express the answer to lowest term.
𝑥 2 +5𝑥−24 𝑥 2 +4𝑥+4
4. 𝑥 2 +6𝑥+8
∙ 𝑥 2 −3𝑥
𝑥 2 −49 𝑥 2 −𝑥−42
5. 2𝑥 2 −3𝑥−5
÷ 𝑥 2 +7𝑥+6
3
𝑥+1
6. 𝑥+4
𝑥2 +11𝑥+10
For problems 7 – 9, perform the indicated operations.
3 𝑥
7. +
𝑥−4 2𝑥+7
2 1 2
8. − 4+
3𝑥 2 9𝑥 𝑥+4
𝑥+10 𝑥
9. (3𝑥+8)3
+ (3𝑥+8)2
Section 2.2: Complex Numbers
For problems 10 – 12, perform the indicated operation and express the answer in rectangular form.
10. 𝑖 2001 − 3𝑖 778
11. 𝑖 45 (2𝑖1995 + 𝑖 1997 )
𝑖 3570 −𝑖 7459
12.
𝑖 888
For problems 13 – 15, perform the indicated operation and write your answer in standard form.
13. (−3 − 𝑖) − (6 − 7𝑖)
14. (2 + 7𝑖)(8 + 3𝑖)
6+7𝑖
15. 8−𝑖
Section 2.3: Functions
For problems 16 – 18, the given functions perform the indicated function evaluations.
16. 𝑓(𝑥) = 3 − 5𝑥 − 2𝑥 2
(a) 𝑓(4)
(b) 𝑓(6 − 𝑡)
(c) 𝑓(7 − 4𝑥)
CEE 200 – Math Plus Page | 3
DEPARTMENT OF ENGINEERING EDUCATION
Computer Engineering Program
UM Visayan Campus, Visayan Village, Tagum City,
Davao del Norte, Philippines
Tel #: (084) 655 - 6074
𝑡
17. 𝑔(𝑡) = 2𝑡+6
(a) 𝑔(−3)
(b) 𝑔(𝑥 2 )
(c) 𝑔(𝑡 + ℎ)
18. ℎ(𝑧) = √1 − 𝑧 2
1
(a) ℎ (2)
(b) ℎ(9𝑧)
(c) ℎ(𝑧 + 𝑘)
Section 2.4: Composition of Functions
For problems 19 – 21, compute (𝑓 ∘ 𝑔)(𝑥) and (𝑔 ∘ 𝑓)(𝑥) for each of the given pair of functions.
19. 𝑓(𝑥) = 4𝑥 − 1, 𝑔(𝑥) = √6 + 7𝑥
20. 𝑓(𝑥) = 5𝑥 + 2, 𝑔(𝑥) = 𝑥 2 − 14𝑥
21. 𝑓(𝑥) = 𝑥 2 + 3, 𝑔(𝑥) = √5 + 𝑥 2
Section 2.5: Inverse Functions
For problems 22 – 24, find the inverse of the functions. Verify your inverse by computing one or both
of the composition as discussed in our class.
22. ℎ(𝑥) = 3 − 29𝑥
23. 𝑅(𝑥) = 𝑥 3 + 6
6−10𝑥
24. 𝑓(𝑥) = 8𝑥+7
CEE 200 – Math Plus Page | 4
