Republic of the Philippines

Department of Education
Region VI – Western Visayas
Division of Silay City
District IV
NAPILAS INTEGRATED SCHOOL
City of Silay
FIRST QUARTER DIAGNOSTIC TEST
S. Y. 2023 – 2024

GENERAL MATHEMATICS 11

Name: __________________________ Date: __________________ Score: __________

I. MULTIPLE CHOICE. Write the letter of the correct answer.

1. Which of the following set of ordered pairs does not illustrate a function?
A. {(1,1),(2,4),(3,9),(4,16),…} C. {(1,-2),(2,-1),(3,0),(4,-1),…}
B. {(1,2),(1,3),(1,4),(1,5),…} D. {(1,2),(2,4),(3,6),(4,8),…}

2. Which of the following are graphs of a function?

I II III
A. I and II B. I and III C. II and III D. I, II and III

3. Evaluate the function 𝑓(𝑥) = 2𝑥 + 3 at 𝑓(−2).

A. 𝑓(−2) = 1 B. 𝑓(−2) = −1 C. 𝑓(−2) = 7 D. 𝑓(−2) = −7

4. Given the function . Find 𝑔(0).

A. 𝑔(0) = 2 B. 𝑔(0) = −2 C. D.

5. Which function has a function value of 𝑓(3) = 5?

A. 𝑓(𝑥) = 𝑥 + 2 B. 𝑓(𝑥) = 𝑥 − 2 C. 𝑓(𝑥) = 2𝑥 − 3 D. 𝑓(𝑥) = 3𝑥 + 2

6. Given 𝑓(𝑥) = 2𝑥 + 3 and 𝑔(𝑥) = 𝑥 − 2, find (𝑓 + 𝑔)(𝑥).

A. (𝑓 + 𝑔)(𝑥) = 3𝑥 + 5 C. (𝑓 + 𝑔)(𝑥) = 3𝑥 + 1
B. (𝑓 + 𝑔)(𝑥) = 3𝑥 − 5 D. (𝑓 + 𝑔)(𝑥) = 3𝑥 − 1

7. Find (𝑓 • 𝑔)(𝑥) given the functions 𝑓(𝑥) = 𝑥 + 4 and 𝑔(𝑥) = 𝑥 − 3.

A. (𝑓 • 𝑔)(𝑥) = 𝑥2 + 𝑥 − 12 C. (𝑓 • 𝑔)(𝑥) = 𝑥2 − 𝑥 + 12
B. (𝑓 • 𝑔)(𝑥) = 𝑥2 − 𝑥 − 12 D. (𝑓 • 𝑔)(𝑥) = 𝑥2 + 𝑥 + 12
8. Given: 𝑓(𝑥) = 3𝑥, and 𝑔(𝑥) = 𝑥 − 2. Which operation on function will result to 𝑓1(𝑥)
= 3𝑥2 − 6𝑥?
A. (𝑓 + 𝑔)(𝑥) B. (𝑓 − 𝑔)(𝑥) C. (𝑓 • 𝑔)(𝑥) D. (𝑓 ∘ 𝑔)(𝑥)
9. Given 𝑓(𝑥) = 2𝑥 − 5 and 𝑔(𝑥) = 𝑥 + 1, find (𝑓 ∘ 𝑔)(𝑥).
A. (𝑓 ∘ 𝑔)(𝑥) = 2𝑥 + 7 C. (𝑓 ∘ 𝑔)(𝑥) = 2𝑥 + 3
B. (𝑓 ∘ 𝑔)(𝑥) = 2𝑥 − 7 D. (𝑓 ∘ 𝑔)(𝑥) = 2𝑥 − 3

10. From the given functions in no. 9, find (𝑔 ∘ 𝑓)(2).

A. 0 B. 1 C. 2 D. 3

11. Given the function 𝑓(𝑥) = 3𝑥 + 1, find (𝑓 ∘ 𝑓 ∘ 𝑓).

A. (𝑓 ∘ 𝑓 ∘ 𝑓) = 9𝑥 + 4 C. (𝑓 ∘ 𝑓 ∘ 𝑓) = 27𝑥 + 4
B. (𝑓 ∘ 𝑓 ∘ 𝑓) = 9𝑥 + 13 D. (𝑓 ∘ 𝑓 ∘ 𝑓) = 27𝑥 + 13
12. A jeepney ride costs Php 9.00 for the first 4 kilometers, and each additional integer
kilometer adds Php 1.00 to the fare. Which piece-wise function represents the
jeepney fare?

A.

B.

C.

D.

13. Given the situation in no. 12, how much would you pay if you travel a distance of 9
kilometers?
A. Php 12.00 B. Php 14.00 C. Php 16.00 D. Php 18.00

14. The velocity in (m/s) of a ball thrown upward seconds after the ball was thrown
is given by . Calculate .
A. 9.8 m B. 10.2 m C. 20 m D. 29.8 m

15. Which of the following is a rational inequality?

A. B. C. D.

16. The mathematical statement is an example of a ___________.

A. Rational equation C. Rational function
B. Rational expression D. Rational inequality

17. Solve for in the equation .

A. 5 B. -5 C. 3 D. -3

18. For what value of x will make the equation true?

A. -1 B. 1 C. -2 D. 2
19. What is the LCD of the denominators in the rational equation
A. B. C. D.

20. Which interval is illustrated by the graph at the right? -1

• ∘
4
A. (- , -1] (4, ) C. (- , -1] [4, )
B. (- -1 4 D. (- , -1) (4, )
21. Which graph illustrates the interval ?
A. C. ∘
-2 5∘
∘
2 •
B.
5
D. -2 • 5 ∘
22. Which is the correct interval notation for the set notation ?
A. B. C. D.

23. An object is to travel a distance of 10 meters. Given the table of values showing
𝑣 for various values of 𝑡, which function below can represent 𝑣 as a function of 𝑡
𝑡 (𝑠𝑒𝑐𝑜𝑛𝑑𝑠) 1 2 4 5 10
𝑣 (𝑚𝑒𝑡𝑒𝑟𝑠 𝑝𝑒𝑟 10 5 2.5 2 1
𝑠𝑒𝑐𝑜𝑛𝑑)

A. 𝑣(𝑡) = 10 + 𝑡 C. 𝑣(𝑡) = 10𝑡

B. 𝑣(𝑡) = 10 − 𝑡 D.
 24. The table of signs and the graph below is for the inequality . Which is its
solution set written in interval notation?
Intervals
Test point

•-3 ∘2
𝑥 −2
𝑥 +3

A. (−∞, −3] ∪ [2, ∞) C. (−∞,−3) ∪ [2, ∞)

B. D.

be the function that describes the concentration of a certain medication

in the bloodstream over time 𝑡. Which table of values represents this function?

A. 𝑡 0 1 2 3 4 C. t 0 1 2 3 4
4 4 4
𝐶(𝑡) 0 1 C(t) 0 1 0
5 5 5

B. D.
𝑡 0 1 2 3 4 t 0 1 2 3 4
5 4
𝐶(𝑡) 0 1 C(t) 0 1 2
4 5

For nos. 26 and 27, refer to the rational function below: 𝒙+𝟏
𝒇(𝒙)=
𝒙−𝟐
26. What is the domain of the function?
A. ℝ except 2 B. ℝ except −2 C. ℝ except 1 D. ℝ except −1

27. What is the range of the function?

A. ℝ except 2 B. ℝ except −2 C. ℝ except 1 D. ℝ except −1

For items 28 – 30, refer to the rational function below:

𝒙𝟐 + 𝟐𝒙 − 𝟏𝟓
𝒇(𝒙) =
𝒙−𝟐
28. What are the zeroes?
A. 𝑥 = 5, 𝑥 = 3 C. 𝑥 = −5,𝑥 = 3
B. 𝑥 = 5, 𝑥 = −3 D. 𝑥 = −5,𝑥 = −3
29. What is the y-intercept?
A. B. C. (0, −15) D. (0,2)
30. What is the vertical asymptote?
A. 𝑥 = −2 B. 𝑥 = 2 C. 𝑥 = −15 D. 𝑥 = 15
31. What is the equation of the vertical asymptote?
A. 𝑥 = −2 B. 𝑥 = −1 C. 𝑥 = 1 D. 𝑥 = 2

32. Based on the figure, at what point on the 𝒚 − 𝒂𝒙𝒊𝒔 did the graph passes through?
A. (0, 3) B. (0, -3) C. ( , 0) D. ( , 0)

33. What is its horizontal asymptote?

A. 𝑦 = 1 B. 𝑦 = 2 C. 𝑦 = 3 D. none
34. What is the value of 𝑦 when 𝑥 = 6?
A. 1 B. 2 C. 3 D. 4

35. Which statement about horizontal asymptotes of a graph of a rational function is

true?
A. 𝑦 = 0 in all rational functions.
B. 𝑦 = 0 if the degree of the numerator and the denominator are the same.
C. 𝑦 = 0 if the degree of the numerator is less than the degree of the numerator.
D. 𝑦 = 0 if the degree of the numerator is greater than the degree of the
denominator.

36. I am a rational function having vertical asymptotes at the lines 𝑥 = 3 and 𝑥 = −3,
and a horizontal asymptote at 𝑦 = 1. If my only 𝑥 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 is at (5, 0) and my
𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 is at , what function am I?

A. B. C. D.

37. Ten goats were set loose in an island and their population growth can be
approximated by the function where 𝑃 represents the goat
population in 𝑡 years. About how many goats will there be
after 5 years?

A. 24 B. 28 C. 32 D. 36

38. Past records from a factory suggest that new employees can assemble 𝑁(𝑡)
components per day after 𝑡 days of being on the job, where . The
maximum number of components that can be assembled cannot exceed what
number?
A. 70 B. 75 C. 80 D. 85

39. Which is not one-to-one function?

A. Student and his LRN C. A person and his birthday.
B. Employee and his SSS number. D. A teacher and his students.

40. Which of the following graphs of a function have inverse functions?

I II III

A. I and II C. II and III

B. I and III D. I, II and III

41. Given the function 𝑓(𝑥) = 5𝑥 + 4, which is its inverse function?

A. 𝑓−1(𝑥) = 4𝑥 − 5 C.
B. D.
 42. Given the function , which is its inverse function?
A. C.
B. D.

43. Given the inverse function . What is the original function?

A.. 𝑓(𝑥) = 2𝑥 + 5 C. 𝑓(𝑥) = 5𝑥 + 2
B. 𝑓(𝑥) = 2𝑥 − 5 D. 𝑓(𝑥) = 5𝑥 − 2

44. Which of the following illustrates the graph of a function and its inverse?
A. C.

B. D.

45. What is the equation of the axis of symmetry into which the graph of the inverse
function is reflected from the graph of the original function?
A. 𝑦 = 𝑥 B. 𝑦 = 0 C. 𝑦 = 1 D. 𝑦 = −1

46. Given the function , what is the domain of the function?

A. ℝ except −3 B. ℝ except 3 C. ℝ except −2 D. ℝ except 2
47. What is the range of the inverse of the function in no. 46?
A. ℝ except −3 B. ℝ except 3 C. ℝ except −2 D. ℝ except 2
For 48 – 50, use the function 𝒇(𝒙) = 𝟑𝒙 + 𝟏
48. What is the inverse of the given function above?

A. 𝑓−1(𝑥) = 𝑥 + 3 C.
B. D. 𝑓−1(𝑥) = 𝑥 − 3

49. Which set of values of 𝒚 corresponds to the assigned values of 𝒙?

𝑥 −2 −1 0 1
𝑦

A. 𝑦 = {−5,−2, 1,4} C. 𝑦 = {−5,−2,−1,4}

B. 𝑦 = {−5,2, 1, 4} D. 𝑦 = {−5,1, 2,4}

50. Which graph illustrates the given function and its inverse?
A. A and B C
B. A and C
C. A and D D
D. B and C