NAME: _________________________________ SECTION: _________________ SCORE: ______________
EXAMINATION IN GENERAL MATHEMATICS
Directions: Read and analyze each of the questions/situations carefully. Write the answer after each
number
1. Which among of the following refers to an equation in two variables x and y, where the variable y may be
expressed as f(x) if every value of x represents the domain corresponds to a single / more value(s) of y which
represents the range?
2. A user is charged P200 monthly for a Globe mobile plan which include 300 free text messages. Messages in
excess of 300 is charged P3.00. Which of the following represent a monthly cost for the mobile plan using s(t) where
t is the number of messages sent in a month.
𝑥−1
3. Which of the following is the value of f( -3 ) that f(x) = 2𝑥+1, ?
4. For what value of y is ( 1 + y, - 3 ) = ( 13 – y , - 3 )?
5. Which of the following is the equivalent expression of (f+g) (x)?
6. If f(x) = 2x - 4 and g(x) = x2 + 2x - 4, what will you do first if you are going to find for the value of g 𝑜 𝑓(−3)?
7. What is ( f – g ) (x) if f(x) = x2 – 3x - 4 and g(x) = 3x2 - 4x + 3,?
𝑓
8. Which of the following is the simplest form of 𝑔 (𝑥) given that f(x) = x2 + 5x – 6 ; and g(x) = x + 6, ?
9. A taxi driver charges passenger P 35.00 as initial fee an additional P2:00 for every 500 meters traveled during
the entire trip. How much will a passenger pay if he traveled a total of 25km?
10. If the temperature in degree Celsius inside the Earth is represented by T(d) = 10d - 20 where (d) is the depth in
kilometers, what is the temperature inside the Earth in 12 kilometers?
11. A truck that delivers essentials in remote areas can travel 85 kilometers. Which of the following expresses the
velocity v as a function of travel time t in hours?
12. Due to the enhanced Community Quarantine, Banawe Foot Spa temporarily stopped its operation and help the
employees the owner decided to split evenly its total revenue of P85, 000. If the number of employees is
represented by x, which function represents the amount received?
13. Which of the following function has the form f(x) =
ℎ(𝑥)
,
𝑔(𝑥)
where h (x) ≠ 0, where g(x) and h(x) are polynomials?
14. Which of the following is NOT an example of a rational function?
A. f(x) =
7x −1
2𝑥
B. f(x) =
𝑥 2 −2𝑥+1
4𝑥+3
C. f(x) =
2𝑥 3 −4𝑥+1
5𝑥
D. f(x) = √5 (𝑥 − 3)3
15. Which of the following is the usual way of eliminating the denominator in solving rational equations?
16. How will you check if the solution you have done in solving rational equations and inequality is correct?
17. Which of the following is a solution of
7𝑥−2
𝑥+6
=
3𝑥+1
?
𝑥
17. Which of the following rational equations best represents the given graph below?
𝑥+4
𝑥+2
𝑥−2
A.
B. y =
C. y =y =
𝑥−2
𝑥−4
𝑥−4
19. Which of the following table represents the rational function y = −𝑥?
A.
x
y
1
-1
2
-2
3
-3
4
-4
B.
x
y
1
1
2
2
3
3
4
4
C.
x
y
1
3
2
5
2
3
7
3
4
9
4
D.
x
y
1
-3
2
5
2
3
7
3
4
9
4
D. y =
𝑥+2
𝑥+4
20. How do you call the writing of the domain/range of a rational function in format (-∞, 1) U (1, ∞)?
2
21. What is the domain of f(x) = 𝑥+5 ?
22. Which of the following are the points of intersection of the graph and the axes?
23. If the degree of the leading coefficient of the numerator is less than to the degree of the leading coefficient of
the denominator of a rational function, which of the following statements has to be TRUE?
A. The slant asymptote is y = 0
B. The horizontal asymptote is y = 1
C. The graph has vertical asymptote
D. The graph has an oblique asymptote
24. Which of the following rational functions have an oblique asymptote?
A. 𝑓(𝑥) =
𝑥 2 −2𝑥 + 5
𝑥−10
𝑥+ 7
B. 𝑓(𝑥) = 𝑥 2 − 2𝑥 + 1
C.𝑓(𝑥) =
3𝑥+2
𝑥+1
𝑥
D. 𝑓(𝑥) = 4𝑥 + 1
25. The sum of two numbers is 8. If x represents one of the numbers and y represents the product of two numbers,
which statement correctly expresses y as a function of x?
26. The rate of a certain boat is 8km/hr in still water. Going upstream, it takes 24 kilometres and for the duration of
the travel, both upstream and downstream, it took 6 hours. What is the speed of the current?
27. Mario was given 3 hours to practice driving is motorcycle. He plans to travel 100 kilometers at an average
speed of 40 kilometers per hour. He wants to maximize his time in driving his motorcycle. How many kilometers
more does he need to travel to spend at most 3 hours?
A. exactly 30 kilometers
B. less than or equal to 20 kilometers
C. less than or equal to 30 kilometers
D. greater than or equal to 20 kilometers
27. The type of functions that describes the pairing of a single x value to a single y value.
29. Which of the following situations implies a one to one function?
A. The rule which assigns to each person his/her friend.
B. The rule which assigns to each month its corresponding number of days.
C. The rule which assigns to each polygon its corresponding number of diagonals.
D. The rule which assigns to each person his/her Taxpayer’ s Identification Number.
30. Which of the following is not involved in the process of finding the inverse of a function?
31. What is the inverse of the given function f(x) = ( 2, 4 ), ( 3, 5 ), ( 4, 6 ), ( 9, 7 ), ( -2, 8 )?
32. A function f is given f(x) = x3 – 1; which of the following is the graph of the given function and its
inverse?
A.
B.
D.
C.
33. Which of the following ordered pairs of an inverse function has its one to one function indicated in the table
below?
x
-2
-1
0
1
2
y
0
1
2
3
4
𝑥−1
34. What is the range of the inverse of the given rational function f(x) = 𝑥−4?
35. Which of the following is the set of all allowable values of the independent variable in a given rational function?
𝑥+ 1
36. Which of the following is the range of the inverse of the function f(x) = 𝑥 − 5?
37. What is/are the domain and range of the rational function f(x) =
1+x
?
x−2
38. Suppose I am travelling at 30 miles per hour and I want to know how I have gone in x hours, this could be
represented by the function f(x) =30 + 2x. What is the inverse of the function?
39. Mark drives his new car 80 kilometers from his residence to the office and spends the week in a company
apartment. He drives back home every Friday. If his car’s odometer shows that he has traveled 1640
kilometers since he bought the car, how many weeks did he drive his car?
40. Which of the following function has an exponent that is a variable?
41. Which of the given situations illustrate an exponential change?
A. As x increases the value of y increases 42.
B. The monthly wage of a laborer increase by 75 every year
C. The number of organisms in a culture doubles every 5 hours
D. A store has 100 regular customers and each month 5 new customers come
42. Which of the following should be considered in solving an exponential equation?
43. What value of x will make 4 2x = 8 x + 6 correct?
44. Which of the following best leads to the value of the unknown in 81x = 9?
45. It is known as the set of all allowable values of the independent variable in a given exponential function.
46. Which of the following does not exist in finding the domain and range of an exponential function?
A. Zero value on the denominator
B. Negative values on the denominator
C. Zero value under the square root sign
D. Positive values under the square root sign
46. Which of the following statement is always true?
A. For any given x-value, the y-value of y = 2x is negative.
B. The domain of exponential function y = 2x is all real numbers.
C. The domain of exponential function y = 2x is positive numbers.
D. For any given x-value, the y-value of y = 2x is all real numbers.
47. What value of x will make the function y = 23x - 81 equal to 0?
A. 2
B. 1
C. 0
D. -1
48. What is the y-intercept of g(x) = −6x+1 + 1?
A. -5
B. -1
D. 7
C. 1
49. Which of the following depicts the increase in number or size at a constantly growing rate?
A. Half-life
B. Time elapsed
C. Exponential decay
D. Exponential growth
50. Suppose ₱6000.00 is invested at 7% interest compounded annually. How much money will there be in the bank
at the end of 8 years?
A. ₱5,352.90
B. ₱5,325.90
C. ₱5,253.90
D. ₱5,235.90