General Mathematics

Solve for the following logarithmic functions: (b) logx 16 = 2 x =

• -4

Which of the following does not represent an exponential function?

• a. The conversion of fahrenheit to celsius
• b. half life of nuclear matter
• c. compound interest of loans acquired
• d. population growth of microorganisms

The graph of a function and its inverse are always reflections of each other in the line y = x

• True
• False

If g(x) = 4|x-3|+2. Find g(1).

• 10

Bananas are sold at Php 50.00 per kilo. Write a function notation that describes this situation.

• a. B(x) = x - 50
• b. B(x) = x / 50
• c. B(x) = 50x
• d. B(x) = x + 50

Which of the following function notation describes the ordered number pair P(x) = {(1,6), (2,11), (3,16), (4,21)}?

• a. f(x) = 5x + 1
• b. f(x) = 5x - 1
• c. f(x) = 11/5x
• d. f(x) = x + 6

f(x)=x+2 f(x)=x+2 | x2 + x - 2

• f + g

f(x)=x+2 f(x)=x+2 | x - 2

• g/f

Let f(x) = 4x-5 and g(x) = 3x, find (fg)(x).

• 12x^2-15x

f(x)=x+2 f(x)=x+2 | 1/x-2

• f/g

(Matching Type) Given f(x) = x + 4 and g(x) = 2x + 1 match the expression to its simplification operation. x+4 / 2x+1

• f/g

Find the solution for each rational equation: 3/x+1 = 2/x-3

• 11

Find the value of the following logarithmic expressions (b) log9 729 =

• 3

One hundred meters of fencing is available to enclose a rectangular area next to a river. Give a function A that can represent the area that can be enclosed in terms of x. Function : A =

• -0.5

3 log9 x2 = 6 log9 x

• True
• False

f(x)=squarerootof(x−3)

• 5

Are the following functions one-to-one? (Answer by typing "Yes" or "No" - without the quotation marks) f(x)=10

• NO

Consider the rational expression f(x)=5x−1−x+2, What is its horizontal asymptote? y =

• -5

Admission price to Enhcanted Kingdom park is Php 600 per person. The average patron attending EK spends about Php 500 on food, drinks, games, and souvenirs. Find the function notation that accurately describes this situation.

• a. E(x) = (600 + 500)x
• b. E(x) = 600 + 500x
• c. E(x) = 600x + 500
• d. E(x) = (600x + 500)x

Given the Function: {(1, 2), (2, 5), (3, 7)}, give the domain and the range. (Note: give the values separated by a space. example: Range: 1 2 3) Domain:

• 1 2 3

Given f(x)=x−2 f(x)=x−2, find the following: f(−1)=

• -3

Let f(x) = 4x-5 and g(x) = 3x, find (f+g)(x).

• 7x-5

Tell whether the following is a characteristic of stocks or bonds: (a) A form of debt financing, or raising money by borrowing from investors.

• Bond

Simplify the given expressions and find the value of x.

• 64

Two race car drivers Ryan and Philip were taking laps around the race track. It was noted that Ryan drove 52.5 miles in the same time that Philip drove 37.5 miles. If Ryan's average speed was 30 mph more than that of Philip, what was Ryan's average speed?

• a. 75 mph
• b. 85 mph
• c. 115 mph
• d. 105 mph

After taking a certain antibiotic, the concentration (C) of the drug in the patient's bloodstream is given by C(x)=(0.04t)/(t2−2)

• a. 4 hours
• b. 3 hours
• c. 5 hours
• d. 2 hours

Solve for the following logarithmic functions: (a) log3 (2x-1) = 2 x =

• 5

Solve for the value of x: 7x+4 = 492x-1 x =

• 2

Find the solution for the rational equation: ((2/(x+1)+5/2x)=2).

• 0 and -1/5

Which of the is the inverse of (f(x) = 4x+12)?

• (f(x) = 12x-4)
• (f(x) = 12x+4)
• (f(x) = (x/4)+3)
• (f(x) = (x/4)-3)

(Matching Type) Given f(x) = x + 4 and g(x) = 2x + 1 match the expression to its simplification operation. 2x+1 / x+4

• g/f

Maya has an internet service that currently has a monthly access fee of Php 999.00 pesos and a connection fee of Php 1.00 per hour. How much will she pay if she was able to use the service for 15 days?

• 1359

All functions have inverse functions.

• True
• False

Given the Function: {(10, 9), (11, 8), (12, 7)}, give the domain and the range. (Note: give the values separated by a space. example: Range: 1 2 3) Range:

• 9 8 7

Solve for the value of x: 4x+2 = 82x x =

• 1

f(x)=x+2 f(x)=x+2 | -x2 + x + 6

• f - g

Consider the rational expression f(x)=5x−1−x+2, What is its vertical asymptote? x =

• 2

(log3 2)(log3 4) = log3 6

• True
• False

What is the zero of the logarithmic function: f(x) = log3 (x-1)? What is the vertical asymptote of the function? x =

• 0

Solve for the following logarithmic functions: and

• 4

Tell whether the following is a characteristic of stocks or bonds: (a) A form of equity financing or raising money by allowing investors to be part owners of the company.

• Stock

Given ƒ(x) = x2 and g(x) = 2x – 3, find (ƒ o g)(x).

• a. 4x2 – 12x + 9
• b. 4x2 - 9
• c. 4x2 + 9
• d. 4x2 + 12x - 9

Given the Function: {(1, 2), (2, 5), (3, 7)}, give the domain and the range. (Note: give the values separated by a space. example: Range: 1 2 3) Range:

• 2 5 7

Are the following functions one-to-one? (Answer by typing "Yes" or "No" - without the quotation marks) f(x)=squarerootof(2−5x8)

• NO

Let f(x) = 4x-5 and g(x) = 3x, find (fog)(x).

• 12x-5
• Solve for the logarithmic expression:
• log7 (73 • 78) = Answer
• 11

The average cost per unit C(x), in dollars, to produce x units of toy cars is given by C(x)=(8000)/(x−50)

• a. $43.60
• b. $56.40
• c. $6.15
• d. $6.67

f(x)=x+2 f(x)=x+2 | x3 + 2x2 - 4x - 8

• f - g

If h (x) = (x + 2)/3, find h(-8).

• a. ½
• b. -½
• c. -2
• d. 2

Given the Function: {(10, 9), (11, 8), (12, 7)}, give the domain and the range. (Note: give the values separated by a space. example: Range: 1 2 3) Domain:

• 10 11 12

Are the following functions one-to-one? (Answer by typing "Yes" or "No" - without the quotation marks) f(x)=x

• YES

Which of the following function notation describes the ordered number pair P(x) = {(1,11), (2,22), (3,33), (4,44)}?

• f(x) = x - 11
• f(x) = 11/x
• f(x) = x + 11
• f(x) = 11x

Let f(x) = -10x-18 and g(x) = -3x, find (f-g)(x).

• -7x-18

Temperatures are normally expressed in degree Celsius in the Philippines and in Fahrenheit in some western countries. If the function for fahrenheit to celsius conversion is (T(°C) = (T(°F) - 32) × 5/9), the celsius to fahrenheit conversion is (T(°F) = (T(°C) × 9/5) + 32). What is the equivalent conversion of 70°F to Celsius?

• 21.11

log3 2x2 = log3 2 + 2 log3 x

• True
• False

Without using a calculator, find the value of the following logarithmic expression.

• 5

If g(x) = (x+2)/3. Find g(-8).

• -2

For the function g(x) = 3x, find g(0) =

• 1

log 22 = (log 2)2

• True
• False

The relation pairing an SSS member to his/her SSS number is a one-to-one function.

• True
• False

(Matching Type) Given f(x) = x + 4 and g(x) = 2x + 1 match the expression to its simplification operation. 2x + 5

• f of g

The absolute value function for the domain of all positive real numbers has an inverse function.

• True
• False

Given ƒ(x) = x2 and g(x) = 2x – 3, compute (ƒ o g)(x); then find (ƒ +g)(2).

• a. 5
• b. 7
• c. 6
• d. 4

Admission price to Universal Studios park is Php 2600 per person. The average patron attending spends about Php 1500 on food, drinks, games, and souvenirs. Find the function notation that accurately describes this situation.

• a. E(x) = (2600x + 1500)x
• b. E(x) = 2600 + 1500x
• c. E(x) = (2600 + 1500)x
• d. E(x) = 2600x + 1500

If g(x) = 3x^2+2x-1. Find g(-1).

• 0

For the function g(x) = 3x, find g(2) =

• 9

The weekly sale S (in thousands of units) for the t^th week after the introduction of the product in the market is given by S=(120t)/(t2+100)

• a. Fourth
• b. Ninth
• c. Tenth
• d. Fifth

y−intercept

• 1

p=(5,125,000V2−449,000V+19307)/(125V2(1,000V−43))

• 0

For the function g(x) = 3x, find g(-2) =

• 1/9

(Matching Type) Given f(x) = x + 4 and g(x) = 2x + 1 match the expression to its simplification operation. 2x2 + 9x + 12

• f∙g

One hundred meters of fencing is available to enclose a rectangular area next to a river. Give a function A that can represent the area that can be enclosed in terms of x. x2 +

• 50

For the function g(x) = 3x, find g(4) =

• 81

What is the zero of the logarithmic function: f(x) = log3 (x-1)? Zero:

• 0

The total cost for playing paintball is Php 100 per gun for rent and Php 1000 per 2000 paintballs. Assuming only 2000 paintballs is allowed for team who will play, which of the following function notation matches the situation?

• a. P(x) = 100x + 2000
• b. P(x) = 100 + 2000x
• c. P(x) = 2000 - 100x
• d. P(x) = 2000x + 100x

The vertical line test is used to determine whether a function is one-to-one when its graph is given.

• True
• False

For the function g(x) = 3x, find g(-4) =

• 1/81

Let f(x) = 4x-5 and g(x) = 3x, find (f/g)(x).

• (4x-5)/3x

f(x)=x+2 f(x)=x+2 | x2 - 2

• f ∘ g

Simplify (4q2r2s3 )3 .

• a. 64q6r6s9
• b. 43q6r6s9
• c. 12q6r6s9
• d. 43q5r5s6

Simplify the expression (-4a2b-1c-2) (2a3b2c-1).

• a. -8a5c3/b
• b. -8a5bc-3
• c. -8a2b
• d. -8a5b/c3

Find g(7) in a function g(x) = x2 -3x – 2.

• a. -9
• b. 26
• c. 9
• d. -5

Which of the following is the inverse of f(x) = ½(3x + 4)?

• a. f-1(y) = ½ (3y-4)
• b. f-1(y) = 2/3 (y-2)
• c. f-1(y) = 2/3 (y-4)
• d. f-1(y) = 1/3 (2y+4)

Evaluate ƒ(x) = /x +2/, given the ƒ(-9).

• a. -11
• b. 7
• c. -7
• d. 11

Find the value of the following logarithmic expressions (c) log5 5 =

• 1

Given the equation (5^(-2x -10) = 25^(x + 1)), solve for the value of x that will make the equation true.

• -3

Find the value of each logarithmic expression. (Note: There's only one answer for the pair of logarithmic expressions indicated below.)

• 5

Temperatures are normally expressed in degree Celsius in the Philippines and in Fahrenheit in some western countries. If the function for fahrenheit to celsius conversion is (T(°C) = (T(°F) - 32) × 5/9), the celsius to fahrenheit conversion is (T(°F) = (T(°C) × 9/5) + 32). Are the two functions inverse of each other? (Note: "Yes" or "No")

• yes

3/(x+1)=2/(x−3)

• 11

Simplify (x2 + 2x – 3) – (x2 – 2x -3).

• a. 4x – 6
• b. 0
• c. 4x
• d. -2x2 -4x – 6

From the table of values, identify which value of x are the zeroes of the function.

• -3 and 2

3(log9 x)2 = 6 log9 x

• True
• False

The relation pairing a real number to its square is a one-to-one function.

• True
• False

Are the following functions one-to-one? (Answer by typing "Yes" or "No" - without the quotation marks) f(x)=5−9x

• YES

If g(x) = -4a+7. Find g(2a).

• -8a+7

The cost of joining a gym membership includes a one time sign-up fee of Php 2000 plus Php 1000 for each month of membership. Which of the following function notations matches this situation?

• a. G(m) = (1000 + 2000)m
• b. G(m) = 2000 + 1000m
• c. None of the given
• d. G(m) = 1000 + 2000m

Given f(x)=x−2 f(x)=x−2, find the following: f(0)=

• -2

Find the value of the following logarithmic expressions (a) log2 32 =

• 5

Temperatures are normally expressed in degree Celsius in the Philippines and in Fahrenheit in some western countries. If the function for fahrenheit to celsius conversion is (T(°C) = (T(°F) - 32) × 5/9), the celsius to fahrenheit conversion is (T(°F) = (T(°C) × 9/5) + 32). What is the equivalent conversion of 0°C to Fahrenheit?

• 32.00

(Matching Type) Given f(x) = x + 4 and g(x) = 2x + 1 match the expression to its simplification operation. 3x + 5

• f + g

(log3 2)(log3 4) = log3 8

• True
• False

Are the following functions one-to-one? (Answer by typing "Yes" or "No" - without the quotation marks) f(x)=3−8x2

• NO

Given f(x)=x−2 f(x)=x−2, find the following: f(3)=

• 1

log3 2x2 = 2 log3 2x

• True
• False

(Matching Type) Given f(x) = x + 4 and g(x) = 2x + 1 match the expression to its simplification operation. -x + 3

• f - g

Temperatures are normally expressed in degree Celsius in the Philippines and in Fahrenheit in some western countries. If the function for fahrenheit to celsius conversion is (T(°C) = (T(°F) - 32) × 5/9), the celsius to fahrenheit conversion is (T(°F) = (T(°C) × 9/5) + 32). What is the equivalent conversion of 68°F to Celsius?

• 20.00