Functions

Question 1

Functions can be applied to describe and analyze the following real-life scenarios:

Answer 1

Thecostyou have to pay after shopping depends on thenumber of itemsyou bought

Theamount of gasolineconsumed depends on thedistance traveled by car

Themonthly sales of a restaurantdepend on thenumber of dishes it sells

Question 2

Example 1:Determine the dependent and independent variables of the following situation:

a. The score of a student in his exam depends on the number of hours he studied

b. The profit of an entrepreneur depends on the number of items he sold

c. The number of participants in a conference tells the number of seats to be prepared by the organizers of the conference

Answer 2

Solution:

a. Independent variable: number of hours the student studied; dependent variable: the score of the student in his exam

b. Independent variable: number of items sold; dependent variable: profit of the entrepreneur

c. Independent variable: number of participants in a conference; dependent variable: number of seats to be prepared

Question 3

Example 2:The battery level of a phone depends on the number of hours it was charged. If the phone is charged for 2 hours, its battery level is 80%. Determine the independent variable, dependent variable, input, and output of this given problem.

Answer 3

Solution:The dependent variable is the battery level of the phone since its value depends on how long or how many hours that phone was charged. The independent variable is the number of hours the phone was charged since it dictates what will be the battery level of the phone.

The input in the given situation is 2 hours since it is a value of the independent variable (number of hours). Meanwhile, 80% is the output since it is a value of the dependent variable (battery level).

Question 4

a relation wherein the first components of the ordered pairs are assigned or matched to only a single second component.

Answer 4

Function

Question 5

Example:Which of the following relations is/are functions?

a. J = {(0, 1), (2, 1), (3, 2)}

b. K = {(5, 1), (5, 2), (5, 3)}

Answer 5

Solution:

a. J is a function since no first component of ordered pairs is repeated.

b. K is not a function since there’s the first component of ordered pairs that are repeated (5 is assigned to two different second components).

c. The diagram shows an example of a function since we can write the pairs as: (1, c), (2, b), (3, a), (4, d), (5, e). No inputs are repeated or matched with two different outputs.

d. The diagram is not a function since two of the first components are matched to two different second components. If we write the given diagram into a set of ordered pairs, we’ll obtain (x, 1), (y, 3), (y, 4), (z, 2), (z, 1). Notice that y and z (which are the first components) are matched with two different second components.

Question 6

For instance, the set of ordered pairs {(1, 2), (2, 4), (3, 6), (4, 8)} is a

Answer 6

Function

Question 7

Example:A small milk tea shop earns Php 40 for every milk tea sold, Php 80 if it sells two milk teas, Php 120 if it sells three milk teas, and so on.

Answer 7

Solution:In this situation, the sales of the milk tea shop are thedependent variablesince its value depends on how many milk teas the shop will sell. This implies that the number of milk teas sold is theindependent variablesince the number of milk teas sold dictates the value of the sales (or dependent variable).

We can express the given set of ordered pairs matching the number of milk teas sold to the number of sales as:

{(1, 40), (2, 80), (3, 120)}

As we can see, the set above is a function.

Question 8

The ______is a function of the independent variable.

Answer 8

Dependent variable

Question 9

We have stated that the sales of the milk tea shop are a function of the number of milk teas sold. In function notation, we express it as:

Answer 9

y = f(x)

Question 10

Example 1:The amount of gasoline (g) consumed by a car in liters is a function of the distance (d) traveled by the car in km. Express this in function notation and determine the independent and dependent variables

Answer 10

Solution:In this situation, the amount of gasoline consumed is the dependent variable while the distance traveled by car is the independent variable. In function notation:

g = f(d)

Question 11

Example 2:Using the function notation above, what does 2 = f(5) mean?

Answer 11

Solution:Sinceg = f(d),then2 = f(5)means that 5 km traveled by car consumes 2 liters of gasoline.

We can express this as an ordered pair (2, 5).

Question 12

Example 1:Evaluate f(x) = x²+ 2x at x = 0.

Answer 12

Solution:

f(x) = x2+ 2

f(0) = (0)2+ 2(0)Input x = 0 to the function

f(0) = 0The output value we obtain is 0

Thus, thevalue of the function is 0when we inputx = 0to it.

Question 13

Example 2:What is f(-1) if f(x) = x – 9?

Answer 13

The symbolf(-1)tells us that we need to substitute or inputx = -1to the function.

Solution:

f(x) = x – 9

f(-1) = (-1) – 9Input x = -1

f(-1) = -10

Thus, thevalue of the function is -10when we inputx = -1to it.

Question 14

Example 3:A video game company’s annual sales in PHP is a function of the number of copies of video games it sold in the market and is described algebraically by the function S(x) = 450x + 10000 where x is the number of copies of video games sold. Suppose that in 2012, the number of video games sold was 13,000. How much were the company’s annual sales in 2012?

Answer 14

Solution:

Given the functionS(x) = 450x + 10000, the annual sales in 2012 can be determined by inputtingx = 13000(i.e., the number of copies of video games sold) into the given function:

S(x) = 450x + 10000

S(13000) = 450(13000) + 10000Input x = 13000

S(13000) = 5,860,000

Hence,in 2012, the video game company generated annual sales of PHP 5,860,000.

Question 15

the set of all possible values of the independent variables in a function.

Answer 15

domain of a function

Question 16

The simplest things to consider when determining the domain of a function are:

Answer 16

The denominator of the function must not be 0.

The value under the square-root sign of the function must be nonnegative (0 or positive).

If the output of a function is always a real number for any real number you input into the function, then the domain of the function is the set of real numbers.

Question 17

Example 1:Determine the domain of the function
f(x) = 2x + 1.

Answer 17

Solution:Since the given function has no denominator and square root sign, then the domain off(x) = 2x + 1 is the set of all real numbers. This means that whatever real number you substitute toxthe value ofyorf(x)will always be a real number.

We can write the set of real numbers as the domain in this set notation form:

This is read as“the domain is the set of all x such that x is an element of the set of real numbers”, with the last symbol being the set of real numbers.

Question 18

Example 2:What is the domain of the function
f(x) = x2– 5x + 6?

Answer 18

Solution:Since the given function has no denominator and square root sign, then the domain off(x) = x2– 5x + 6is the set of all real numbers. This means that whatever real number you substitute toxthe value ofyorf(x)will always be a real number.

In set notation form,
D={x|x € R|}

Question 19

Example 3:Determine the domain of

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

Answer 19

Solution:This time, the given function has a denominator which isx – 1. To determine the domain of this function, let us determine first the value ofxthat will make the denominatorx – 1equal to 0.

We can set up an equation:

x – 1 = 0

x = 1Transposition method

Thus, atx = 1, the denominator of the given function is 0.

The value ofxthat will make the denominator 0 will be the value excluded in the domain. Hence, the domain of the function is the set of all real numbers except 1.

Any number you substitute toxwill give you a real number value of function except for 1 because, atx = 1, the denominator will be 0 (which is not allowed since division by 0 is undefined).

In set notation form,

This is read as“the domain is the set of all x such that x is an element of the set of real numbers except 1″.

Question 20

Example 4:Determine the domain of

f(x)= 9-x/x+15

Answer 20

Solution:We need to find the number that must be excluded in the domain. That number is what will make the denominator 0.

x + 15 = 0

x = -15Transposition method

Therefore, the domain is the set of all real numbers except -15.

In set notation form,
D={x|x € R-15}

Question 21

Example 5:What is the domain of

f(x)=sqrt(9-x)

Answer 21

Solution:The given function has a square root sign. To find the domain of this function, we must find all values ofxthat will make theradicand(the quantity under the radical sign) nonnegative.

Why do we need to make the radicand nonnegative?Because if the radicand is negative, we have a square root of a negative number which is animaginary numberand not a real number.

This means that we need to find the values ofxsuch that9 – xwill be nonnegative or greater than or equal to 0.

Thus, the domain of the function is the set of all real numbers less than or equal to 9. This means that if you try to substitute a value ofxthat is greater than 9, the value of the function will not be a real number (try to substitute x = 10 to the function and see what will happen).

In set notation form,

D = { x | x ≤ 9}

Question 22

Example 6:Determine the domain of the function

f(x)=sqrt(x-2)/x-8

Answer 22

Solution:As you can see, the given function has a denominator and a square root sign, hence making it quite tricky.

Let us work for the domain of this function using the considerations one by one:

Starting with the numerator, recall that if we have a square root sign, the radicand must be nonnegative:

x – 2 ≥ 0

x ≥ 2Transposition method

Thus, part of our domain is the set of all real numbers greater than 2.

We’re not done yet as we need to consider the denominator as well.

The denominator must not be zero, so we have:

x – 8 = 0

x = 8Transposition method

Thus, we should excludex = 8from the domain since it will give a denominator value of 0.

Note that we obtainedx ≥ 2earlier and we also discovered thatx = 8should be excluded from the domain. Therefore, our domain should bex≥2 \ 8, orthe set of all real numbers greater than 2 but 8 is not included.

In set notation form,

D = {x | x ≥ 2 \ 8}

Question 23

the set of all possible values of the dependent variable.

Answer 23

Range

Question 24

Example 1:If f(x) = x + 3 and g(x) = x + 5, what is (f + g)(x)?

Answer 24

Solution:

(f + g)(x) = f(x) + g(x)

(f + g)(x) = (x + 3) + (x + 5)

(f + g)(x) = 2x + 8

The answer is(f + g)(x) = 2x + 8

Question 25

Example 2: Determine (f + g)(1) using the same functions in the previous example. If f(x) = x + 3 and g(x) = x + 5, what is (f + g)(x)?

Answer 25

Solution: The symbol (f + g)(1) means that we need to input 1 to the sum function (f + g)(x). Recall that we obtain (f + g)(x) = 2x + 8 in the previous example. Hence, to determine (f + g)(1): (f + g)(x) = 2x + 8 (f + g)(1) = 2(1) + 8 (f + g)(1) = 2 + 8 (f + g)(1) = 10 Thus, (f + g)(1) = 10

Question 26

Example 3: If f(x) = 5x – 2 and g(x) = 3x + 4. Determine (f – g)(2).

Answer 26

Solution: Let us start by determining (f – g)(x) first: (f – g)(x) = f(x) – g(x) (f – g)(x) = (5x – 2) – (3x + 4) (f – g)(x) = (5x – 2) + (-3x – 4) (f – g)(x)  = 2x – 6 Thus, (f – g)(x)  = 2x – 6. To find (f -g)(2), we input x = 2 to the difference function: (f – g)(2) = 2(2) – 6 (f – g)(2) = 4 – 6 (f – g)(2) = -2 Therefore, the value of (f – g)(2) is -2.

Question 27

Example 4: if f(x)= x+3/2x and g(x) = x-1/x determine (f + g)(1)

Answer 27

Solution: Since the functions are in the form of rational expressions, we just add the terms of the function just like what we do with rational expressions (Note that the rational expressions are dissimilar so we have to transform them into similar rational expressions first): Now, let us input x = 1 to the sum function to determine (f + g)(1): =2

Question 28

Example 1: If f(x) = 3x and g(x) = x + 1, determine (f ⋅ g)(x).

Answer 28

Solution: Since (f ⋅ g)(x) = f(x) ⋅ g(x), then: (f ⋅ g)(x) = f(x) ∙ g(x) (f ∙ g)(x) = 3x(x + 1) (f ∙ g)(x) = 3x2 + 3x Thus, (f ∙ g)(x) = 3x2 + 3x

Question 29

Example 2: If f(x) = x – 1 and g(x) = x + 4, what is (f ∙ g)(-1)?

Answer 29

Solution: To find (f ∙ g)(-1), we need to determine (f ∙ g)(x) first: (f ∙ g)(x) = f(x) ∙ g(x) (f ∙ g)(x) = (x – 1)(x + 4) (f ∙ g)(x) = x2 + 3x – 4 Using FOIL method Now, we have obtained (f ∙ g)(x) = x2 + 3x – 4 as the product function. To determine (f ∙ g)(-1), we need to input x = -1 to the product function: (f ∙ g)(x) = x2 + 3x – 4 (f ∙ g)(-1) = (-1)2 + 3(-1) – 4 (f ∙ g)(-1) = 1 – 3 – 4 (f ∙ g)(-1) = -6 Therefore, (f ∙ g)(-1) = -6 is the answer.

Question 30

Example 3: If(x)=x-5/x and g(x)=3/x+2 determine (f•g)(2)

Answer 30

Solution: To find (f ∙ g)(2), we have to discover first what is (f ∙ g)(x). We do this by multiplying the given functions: Now, to determine (f ∙ g)(2), we input x = 2 to the product function: Hence, (f ∙ g)(2) = -9/8

Question 31

Example 1: If f(x) = 8x2 + 4x and g(x) = 2x, determine (f⁄g)(x).

Answer 31

To find (f⁄g)(x), we have to divide the function f(x) by g(x): Thus, the answer is (f⁄g)(x)=  4x + 2

Question 32

Example 2: Determine (f/g)(-1) using the same functions provided in the previous example.

Answer 32

Solution: The quotient function we have obtained in the previous example is (f⁄g)(x) = 4x + 2. To find (f⁄g)(-1), we have to substitute or input x = -1 to the quotient function. (f⁄g)(x)=  4x + 2 (f⁄g)(-1)=  4(-1) + 2 (f⁄g)(-1)=  -4 + 2 (f⁄g)(-1)=  -2 Thus, the value of (f/g)(x) when x = -1 is -2.

Question 33

Example 3: Determine (f/g)(-3) given that f(x) = 2+x/x and g(x)=1/x

Answer 33

Solution: To determine (f⁄g)(-3), we have to find out first the quotient function (f⁄g)(x): From our computation above,  (f⁄g)(x) = 2 + x. To compute for (f⁄g)(-3), we have to input x = -3 to the quotient function: (f⁄g)(-3) = 2 + x (f⁄g)(-3) = 2 + (-3) = -1 The answer is -1.

Question 34

Example 1: If f(x) = 2x – 1 and g(x) = x2 + 3. Determine (f ∘ g)(x).

Answer 34

Solution: The symbol (f ∘ g)(x) tells us that g(x) will be the input of f(x) to obtain the composition or f(g(x)). (f ∘ g)(x) = f(g(x)) To find f(g(x)): f(x) = 2x – 1 f(g(x)) = 2(x2 + 3) – 1 We input g(x) to f(x) f(g(x)) = 2x2 + 6 – 1 f(g(x)) = 2x2 + 5 The answer is f(g(x)) = 2x2 + 5

Question 35

Example 2: If f(x) = 2x – 1 and g(x) = x² + 3. Determine (g ∘ f)(x).

Answer 35

Solution: The symbol (g ∘ f)(x) tells us that f(x) will be the input of g(x) to obtain the composition or g(f(x)). (g ∘ f)(x) = g(f(x)) To find g(f(x)): g(x) = x2 + 3 g(f(x)) = (2x – 1)2 + 3 We input f(x) to g(x) g(f(x)) = (4x2 – 4x + 1) + 3 Square of binomial g(f(x)) = 4x2 – 4x + 4

Question 36

Example 3: Using the same functions in the previous example, determine (g ∘ f)(0).

Answer 36

Solution: The symbol (g ∘ f)(0) just tells us that we need to input 0 to the composition of function (g ∘ f) or g(f(x)). From the previous example, we have obtained (g ∘ f)(x) = g(f(x)) = 4x2 – 4x + 4 Let us now determine (g ∘ f)(0): (g ∘ f)(0) = g(f(0)) = 4(0)2 – 4(0) + 4 = 4 Therefore, the answer is 4.

Question 37

function that is formed by interchanging the independent variable and dependent variable of the original function. 

Answer 37

Inverse function

Question 38

To find the inverse of a function, follow these steps:

Answer 38

Write f(x) as y. Interchange x and y in the function. Solve for y in terms of x to solve for the inverse. Write y as f-1(x) in the final answer.

Question 39

Example: Determine the inverse of f(x) = 2x – 3.

Answer 39

Solution: Step 1: Write f(x) as y. As per instruction, we write f(x) = 2x – 3 as y = 2x – 3. Step 2: Interchange x and y in the function. Interchanging x and y in y = 2x – 3 will give us x = 2y – 3. Step 3: Solve for y in terms of x to solve for the inverse. Write y as f-1(x) in the final answer, Solving y in terms of x means that we need to isolate y from other quantities. =x+3/2

Question 40

one of the simplest functions in mathematics. This function is defined as f(x) = x which means that whatever you input to the function, you will obtain an output equal to that input.

Answer 40

Identity Function

Question 41

a function such that the exponents of its variable are all nonnegative integers. In simple words, this function is expressed in the form of a polynomial.

Answer 41

Polynomial Function

Question 42

a polynomial function wherein the largest exponent of the variable is 1. 

Answer 42

Linear Function

Question 43

the value of x such that f(x) = 0. In other words, this is what you should input to the function so that the output will be 0.

Answer 43

Zero of a Linear Function

Question 44

Example: Find the zero of f(x) = 3x – 6.

Answer 44

Solution: To find the zero of f(x) = 3x – 6, we set f(x) = 0 then solve for x: f(x) = 3x – 6 0 = 3x – 6 Set f(x) = 0 -3x = -6 x = 2 Therefore, the zero of the function f(x) = 3x – 6 is x = 2.

Question 45

Problem 1: A taxi charges fare in this manner: you have to pay a fixed amount of PHP 30 and PHP 10 for every kilometer you have traveled. How much would you have to pay if you traveled 5 km, 7 km, and 10 km?

Answer 45

Solution: We can actually express the situation in the given problem as a linear function. Let x be the number of kilometers you have traveled. Then, let 10x represent the amount you have to pay for the x kilometer you have traveled. Our linear function is f(x) = 30 + 10x where f(x) is the amount you have to pay after traveling for x kilometers. If you travel 5 km: f(x) = 30 + 10x f(5) = 30 + 10(5) f(5) = 30 + 50  f(5) = 80 Hence, you have to pay PHP 80 if you travel 5 km. Now, can you compute how much you have to pay if you travel 7 km or 10 km using the function above?

Question 46

Problem 2: You are planning to buy homemade leche flan from Lena’s Shop. The store charges PHP 65 for every order of leche flan and a fixed amount of PHP 25 as the service fee. Create a function that will show how much you have to pay Lena’s Shop if you plan to buy x orders of leche flan. Determine also how much you will pay if you buy 10 orders of leche flan.

Answer 46

Solution: Let x represent the number of orders of leche flan you’re buying. This means that 65x represents the amount you have to pay for x orders of leche flan you will be buying. Our linear function is f(x) = 65x + 25 where f(x) represents the total amount you have to pay for x orders of leche flan including the service fee. If you buy 10 orders of leche flan, that is, x = 10: f(10) = 65(10) + 25 f(10) = 650 + 25 f(10) = 675 Therefore, you have to pay PHP 675 for 10 orders of leche flan.

Question 47

a polynomial function wherein the largest exponent of its variable is 2. 

Answer 47

A quadratic function

Question 48

Example: Determine the values of a, b, and c (coefficient of each term) of the following: f(x) = x² – 7x + 12 f(x) = 9 – x²

Answer 48

Solution: The quadratic term of f(x) = x2 – 7x + 12 is x2 so a = 1. The linear term is -7x so b = -7. Lastly, the constant term is 12 so c = 12.The quadratic term of f(x) = 9 – x2 is -x2 so a = -1. There’s no linear term in f(x) = 9 – x2 so b = 0. Lastly, the constant term is 9 so c = 9.

Question 49

Example: What is the domain of f(x) = x² – 3x + 1?

Answer 49

Solution: Since the function is a quadratic function, then its domain is the set of real numbers. In set notation: D = {x | x  ∈  R}

Question 50

to find the range of a quadratic function, follow these three steps:

Answer 50

1. Determine the values of a, b, and c. 2. Look at the sign of a first. If a > 0, then you will use R = {y | y ≥ k} as the range.If a < 0, use R = {y | y ≤ k}. 3. Compute the value of k using the values of a, b, and c. Note that k = (4ac – b2) / 4a

Question 51

Example: Determine the range of f(x) = 4x² – 2x + 1.

Answer 51

Solution: Step 1: Determine the values of a, b, and c. We have a = 4, b = -2, and c = 1. Step 2: Look at the sign of a first. The value of a is 4. This implies that a > 0. Hence, we use R = {y | y ≥ k}. Step 3: Compute the value of k using the values of a, b, and c. We compute the value of k using k = (4ac – b2) / 4a. Again, we have  a = 4, b = -2, and c = 1. Using these values, we obtain: k =  (4ac – b2) / 4a k = (4(4)(1) – (-2)2) / 4(4) k = (16 – 4) / 16 k = 12 / 16 or ¾  k = ¾ This means that the range of the quadratic function should be R = {y | y ≥ ¾ } It implies that whatever real number x you input to f(x) = 4x2 – 2x + 1, the values of f(x) or y that you will obtain will always be greater than or equal to ¾. It is impossible to have an output value less than ¾ whatever real number x you input.

Question 52

the values of x such that f(x) = 0. In other words, these are the input values of the function that will provide an output value of 0.

Answer 52

Zeros of a Quadratic Function

Question 53

Example: Determine the zeros of the function f(x) = x² – 7x + 12.

Answer 53

Solution: To find the zeros of the given function, we let f(x) = 0 and then solve for x: f(x) = x2 – 7x + 12 0 = x2 – 7x + 12 0 = (x – 4)(x – 3) By factoring x – 4 = 0 x – 3 = 0 Set each factor to 0 x1 = 4 x2 = 3 Thus, the zeros of the function  f(x) = x2 – 7x + 12 are x = 4 and x = 3.

Question 54

a function that involves an absolute value sign

Answer 54

Absolute Value Function

Question 55

Example 1: Determine f(-1) if f(x) = |x – 3|

Answer 55

Solution: f(x) = | x – 3 | f(-1) = | (-1) – 3 | f(-1) = | -4|  f(-1) = 4 Absolute value is always nonnegative The answer is 4.

Question 56

Example 2: Compute for f(0) if f(x) = |x – 9| + 7

Answer 56

Solution: f(x) = |x – 9| + 7 f(0) = |(0) – 9| + 7 f(0) = | – 9 | + 7 f(0) = 9 + 7 f(0) = 16 The answer is 16

Question 57

The Range of the Absolute Value function can be determined this way:

Answer 57

a. If the form is f(x) = a|x – h| + k, where k is a real number, then the range will be {y | y < k} if a is negative. b. If the form is f(x) = a|x – h| + k, where k is a real number, then the range will be {y | y > k} if a is positive.

Question 58

Example 1: What is the domain and range of f(x) = |x – 3|?

Answer 58

Solution: The domain of f(x) is just the set of all real numbers or D = {x | x ∈ R}  On the other hand, let us determine the range. Since the function is in form f(x) = a|x – h| + k, where a is positive and k = 0, then the range is just the set of all nonnegative numbers or R = {y | y  > 0}.

Question 59

Example 2: What is the domain and range of f(x) = – |x + 1| – 5?

Answer 59

Solution: The domain of f(x) is just the set of all real numbers or D = {x | x ∈ R}  Since the function is in form f(x) = a|x – h| + k, where a is negative and k = 0, then the range is the set of all numbers less than or equal to -5 or R = {y | y < -5}.

Question 60

a ratio of two polynomial functions. Think of it as a function in a fractional form wherein the numerator and denominator are polynomials.

Answer 60

Rational Function

Question 61

is a function that contains a radical sign. One of the widely known types of radical functions is the square-root function, one that involves a square-root sign.

Answer 61

Radical Function

Question 62

functions include exponential functions, logarithmic functions, and trigonometric functions. Exponential and logarithmic functions are beyond the scope of our reviewer. 

Answer 62

Transcendental Function

Question 63

1) The domain of the function 𝑓(𝑥)=2-x/x+4 is? a) D = {x | x ∈ ℜ, x≠-4} b) D = {x | x ∈ ℜ, x > 4} c) D = {x | x ∈ ℜ, x≠½} d) D = {x | x ∈ ℜ, x≠4}

Answer 63

A

Question 64

2) Which of the following is the inverse of the function f(x) = 2x - 1? a) f-1(x) =𝑥 − 1/2 b) f-1(x) =𝑥 + 1/2 c) f-1(x) = x + 2 d) f-1(x) =𝑥 + 2/2

Answer 64

B

Question 65

3) Matt, an avid plantito, plans to buy flower pots for his mini garden. He is planning to buy those flower pots from Jessica’s flower shop. A flower pot costs Php 70 each. Jessica also charges a fixed delivery fee amount of Php 40 regardless of how many flower pots a customer buys. Write a function that will represent Matt’s total cost if he will buy x number of flower pots. a) C(x) = 40x + 70 b) C(x) = 70x - 40 c) C(x) = 40x - 70 d) C(x) = 70x + 40

Answer 65

D

Question 66

4) Using the function you have derived in item #3, determine how much will Matt’s total cost if he will buy 8 flower pots from Jessica’s flower shop. a) Php 600 b) Php 800 c) Php 1000 d) Php 1400

Answer 66

A

Question 67

5) What is the domain of the function f(x) = x2- 3x + 1? a) set of all real numbers b) set of all negative numbers c) set of all nonnegative numbers d) None of the above

Answer 67

A