1ST-LONG-QUIZ_STEM (1).pdf

1st Semester SY 2024 - 2025 FIRST LONG QUIZ GENERAL MATHEMATICS 1. Which of the following relations is a function? A. {(1,3), (−1,5), (2,3), (2,5)} C. {(−1,3), (−1,5), (2,3), (2,5)} B....

1st Semester SY 2024 - 2025 FIRST LONG QUIZ GENERAL MATHEMATICS 1. Which of the following relations is a function? A. {(1,3), (−1,5), (2,3), (2,5)} C. {(−1,3), (−1,5), (2,3), (2,5)} B. {(−2,1), (5,1), (2,1), (11,1)} D. {(2,3), (−1,5), (3,3), (3,5)} 2. All functions are relations but not all relations are functions. A. True C. False B. None of the above D. No clue 2 3 1 3. The LCD of the rational expressions 𝑥, 2𝑥 and 3 is 6x2 A. True C. Maybe B. No idea D. False 𝑥 2 +𝑥−2 4. Determine the zero of the function 𝑔(𝑥) = 𝑥 2 −1 A. x = −2 B. x = −4 C. x = 3 D. x = 1 6 5. Give the domain of the function defined by 3𝑥+6 A. (−∞, −3) ∪ (−3, ∞) B. (−∞, 2) ∪ (2, ∞) C. (−∞, 2) ∪ (−2, ∞) D. (∞, 2) ∪ (2, ∞) 3+8𝑥 2 6. Find the horizontal asymptote of 𝑣(𝑥) = 𝑥 2 +1 A. y = 8 B. y = 2 C. y = 1 D. y = 0 7. What makes this a rational function, 𝑓(𝑥) = √𝑥 2 − 3 ? A. 𝑓(𝑥) B. √𝑥 2 − 3 C. Not a function D. 𝑥 2 − 3 2𝑥+3 8. Give the range of the function defined by 𝑦 = 𝑥. A. (−∞, −2) ∪ (∞, 2) B. (−∞, 2) ∪ (2, ∞) C. (−∞, 2) ∪ (∞, −2) D. (−∞, 2) ∪ (∞, 2) 9. Which of the following graphs represent/s function? A. both A and B B. both A and C C. both B and C D. both B and D 10. Which of the following tables is NOT a representation of a function? A. B. C. D. For items 11 to 12. Consider the functions f and g defined by 𝑓(𝑥) = 2𝑥 − 1 and 𝑔(𝑥) = 𝑥 2. 11. What is the value of (𝑔 − 𝑓)(4)? A. 7 C. -5 B. -7 D. 9 12. What is (𝑔 ○ 𝑔)(−2𝑥)? A. 𝒙𝟐 C. 𝟐𝒙𝟐 B. 𝒙𝟒 D. 𝟒𝒙 13. Given 𝑓(𝑥) = 3𝑥 − 1 𝑎𝑛𝑑 𝑔(𝑥) = 9 − 3𝑥 2 , find (𝑓 ○ 𝑔)(−2) A. −7 C. 5 B. −9 D. 1 1 𝑓(𝑥) 14. Given 𝑓(𝑥) = 𝑥 𝑎𝑛𝑑 𝑔(𝑥) = −𝑥, find 𝑔(𝑥) , 𝑔(𝑥) ≠ 0. A. 𝑥 2 C. − 𝑥 1 B. 𝑥 D. 1 𝑥2 15. If 𝑓(𝑥) = 𝑥 2 + 2 and 𝑔(𝑥) = 𝑥 3 − 1 find 𝑓(4) − 𝑔(4). A. 44 C. −44 B. 45 D. −45 For nos. 16 – 25. Perform the indicated operations: 𝑓(𝑥) = 5𝑥 + 1 𝑔(𝑥) = 5𝑥 − 1 ℎ(𝑥) = 10𝑥2 + 13𝑥 − 3 16-17. (𝑓 + 𝑔)(𝑥) a. 99 18-19. (𝑔 ○ ℎ)(−1) b. 10x 20-21. (𝑓 ∗ 𝑔)(−2) c. 110 22-23. (ℎ − 𝑓)(3) d. 11 24-25. ℎ ( )(4) e. -31 𝑔 For nos. 26–27. Solve for x for the given rational equation. 4𝑥−8 8 26. 4 =𝑥 A. 4 and -2 C. 4 and 2 B. 4 and 2 D. -4 and -2 7 15 3 27. 7𝑥+7 − 5𝑥+5 =9 A. x = 6 C. x = −7 B. x = −6 D. x = −8 28. Give a function that can represent the amount of battery charge of a cellular phone in hour, if 12% of battery was loss every hour. A. 𝑏(ℎ) = 100% − 12%ℎ C. 𝑏(ℎ) = 12%ℎ B. 𝑏(ℎ) = 100% + 12%ℎ D. 𝑏(ℎ) = 100% − 12% − ℎ 𝑥 2 −3𝑥+2 29. What is the Domain of 𝑦 = 𝑥−3 A. 𝑥 = 3 C. 𝑥 = −1 B. 𝑥 = −3 D. 𝑥 = 1 2 2𝑥 2 −𝑥+1 30. Find the vertical asymptote of 𝑔(𝑥) = 𝑥 2 −6𝑥+9 A. x = 3 C. x = 2 B. x = 1 D. x = 0  Key Answer 1. B 11. D 26. A 2. A 12. 𝟏𝟔𝒙𝟒 27. C 3. D 13. -10 28. A 4. A 1 14. − 𝑥 2 29. A 5. (−∞, −2) ∪ (−2, ∞) 15. D 30. A 6. A 16-17. B 7. C 18-19. E 8. B 20-21. A 9. B 22-23. C 10. A 24-25. D