What is the closest definition of a function?

A function relates an input to an output.

An equation that has a dependent variable inside the parenthesis

An equation in which the x is always dependent

What is the set builder notation of A ={ 4,9,16,25} ?

A = { x | x are the squares between 1 and 36}

A = { x | x are the even numbers from 1 to 40}

A = { x | x are the squares from 1 and 36}

A = { x | x are the squares between 1 and 40}

Functions And Relations Test!

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| By Pam Agapay

Pam Agapay

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Quizzes Created: 3 | Total Attempts: 3,260

| Attempts: 857

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1/19 Questions

What is the closest definition of a function?
- A function relates an input to an output.
- An equation that has a dependent variable inside the parenthesis
- An equation in which the x is always dependent

About This Quiz

The 'Functions And Relations Test!' evaluates understanding of fundamental mathematical concepts including functions, relations, and set operations. It tests the ability to differentiate between sets, functions, and relations and solve problems related to set operations, enhancing logical reasoning and mathematical skills.

2.

It is the collection of related objects thru an ordered pair.
- Set
- Relation
- Function
Correct Answer

A. Relation

Explanation

A relation is a collection of related objects, where each object is paired with another object in an ordered pair. This means that there is a connection or association between the objects in the relation. A relation can be represented by a set of ordered pairs, where the first element of each pair is taken from one set and the second element is taken from another set. Therefore, the given explanation correctly describes a relation as a collection of related objects through an ordered pair.

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1
3.

Is a group of objects with the same characteristics.
- Set
- Relation
- Function
Correct Answer

A. Set

Explanation

A set is a group of objects that share the same characteristics. In a set, each object is unique and there is no specific order or arrangement. Sets are commonly used in mathematics to represent collections of elements or to define certain properties. For example, a set of numbers can include all the even numbers or all the prime numbers. Sets can also be used to represent groups of objects in other fields, such as a set of colors or a set of animals.

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1
4.

Given U={1 , 2,3,5,8,9,12 ,13} A={ 1,2,3} B= { 5 , 12 ,13 } what is A - B?
- U
- A
- B
- Null
Correct Answer

A. A

Explanation

The correct answer is A because A - B represents the set of elements that are in A but not in B. In this case, A - B would be {1, 2, 3} since these elements are in A but not in B.

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1
5.

Given U={1 , 2,3,5,8,9,12 ,13} A={ 1,2,3} B= { 5 , 12 ,13 ,8,9} what is B - U?
- U
- A
- B
- Null
Correct Answer

A. Null

Explanation

The set B - U represents the elements in set B that are not present in set U. In this case, all the elements in set B (5, 12, 13, 8, 9) are also present in set U. Therefore, there are no elements in set B that are not present in set U, resulting in an empty set. Hence, the answer is null.

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6.

Given U={1 , 2,3,5,8,9,12 ,13} A={ 1,2,3} B= { 5 , 12 ,13 } what is U - B?
- U
- A
- B
- NULL
Correct Answer

A. A

Explanation

The given question is asking for the set difference between U and B. Set difference is the set of elements that are in the first set (U) but not in the second set (B). In this case, U - B would be the set {1, 2, 3, 8, 9}, as these elements are present in U but not in B.

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0
7.

Collections in a set need to be ordered.
- True
- False
Correct Answer

A. False

Explanation

Collections in a set do not need to be ordered. Sets are an unordered collection of unique elements. The elements in a set are not stored in any particular order and do not have any specific position. The main characteristic of a set is that it does not allow duplicate elements, but it does not require any specific order for the elements. Therefore, the statement "Collections in a set need to be ordered" is false.

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8.

The Universe contains all the possible values in a set.
- True
- False
Correct Answer

A. True

Explanation

The statement is true because the universe, in the context of set theory, refers to the entire set of elements under consideration. Therefore, it contains all possible values that can be included in the set.

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1
9.

The following is presented in what set notation? A = { 2, 3, 4,5 }
- Set Builder
- Roster Form
- Normal Form
Correct Answer

A. Roster Form

Explanation

The given set A = { 2, 3, 4, 5 } is presented in roster form. Roster form is a way of representing a set by listing all its elements within curly braces. In this case, the elements 2, 3, 4, and 5 are listed within the curly braces to represent the set A.

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10.

What is the set builder notation of A ={ 4,9,16,25} ?
- A = { x | x are the even numbers from 1 to 40}
- A = { x | x are the squares from 1 and 36}
- A = { x | x are the squares between 1 and 36}
- A = { x | x are the squares between 1 and 40}
Correct Answer

A. A = { x | x are the squares between 1 and 36}

Explanation

The correct answer is A = { x | x are the squares between 1 and 36}. This is because the set A is defined as the set of squares between 1 and 36, and the set builder notation represents this by stating that x belongs to the set A if x is a square between 1 and 36.

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1
11.

What is f ^-1 of f(x)= 2x + 3?
- X/2 + 3
- Y/2 - 3
- 3y -2
- 3 - 2x
Correct Answer

A. Y/2 - 3

Explanation

The given function f(x) = 2x + 3 represents a linear equation. To find the inverse of this function, we need to swap the x and y variables and solve for y. By doing this, we get x = 2y + 3. Rearranging the equation, we have 2y = x - 3. Dividing both sides by 2, we get y = (x/2) - 3. Therefore, the inverse of f(x) = 2x + 3 is y/2 - 3.

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1
12.

What is the set notation ( letter symbol) for Integers?

Correct Answer
z

Explanation
The set notation for Integers is represented by the letter symbol "z". In mathematics, the set of Integers includes all whole numbers, both positive and negative, as well as zero. The letter "z" is commonly used to represent this set in mathematical notation.

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13.

In a function, x can have one or more elements in Y.
- True
- False
Correct Answer

A. False

Explanation

This statement is false because in a function, each element in the domain (x) can only have one corresponding element in the range (Y). This is known as the one-to-one mapping property of functions. If x had more than one element mapping to Y, it would violate this property and would not be a function. Therefore, the correct answer is false.

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1
14.

Relations are presented through ordered pairs.
- True
- False
Correct Answer

A. True

Explanation

Relations are a way to represent the connection or association between two sets of elements. In mathematics, relations are commonly presented through ordered pairs, where each pair consists of an element from the first set and an element from the second set. This allows us to clearly define and understand the relationship between the elements. Therefore, the statement that relations are presented through ordered pairs is true.

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15.

What is g(f(x)) when f(x) = 2x +3 and g(x) = x -1?
- 2x-1
- 2(x+1)
- 2x + 1
- 2(x -1)
Correct Answer

A. 2(x+1)

Explanation

The given question asks for the value of g(f(x)) when f(x) = 2x + 3 and g(x) = x - 1. To find this value, we substitute f(x) into g(x), which gives us g(f(x)) = g(2x + 3). Plugging in 2x + 3 into g(x), we get g(f(x)) = (2x + 3) - 1 = 2x + 2. Therefore, the correct answer is 2(x + 1).

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2
16.

What property of relationship is shown by the figure below?
- Reflexive
- Transitive
- Symmetric
Correct Answer

A. Transitive

Explanation

The figure shown in the question represents a relationship that is transitive. Transitivity in a relationship means that if there is a connection between two elements A and B, and another connection between elements B and C, then there must also be a connection between elements A and C. In the given figure, it can be observed that whenever there is a connection between two elements, the connection is also present between their corresponding elements, indicating transitivity.

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17.

What type of function is shown by the figure below?
- One to one
- Onto
- Bijection
- Not a function
Correct Answer

A. Onto

Explanation

The figure represents an onto function. An onto function, also known as a surjective function, is a type of function where every element in the range has a corresponding element in the domain. In other words, for every element in the range, there is at least one element in the domain that maps to it. The figure shows that every element in the range is covered by the function, indicating that it is onto.

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18.

What type of function is shown by the figure below?
- One to one
- Onto
- Bijection
- Not a function
Correct Answer

A. Bijection

Explanation

The figure shown represents a function that is both one-to-one and onto. A bijection is a function that is both injective (one-to-one) and surjective (onto). This means that each element in the domain is mapped to a unique element in the codomain, and every element in the codomain is mapped to by at least one element in the domain. Therefore, the correct answer is bijection.

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19.

What type of function is shown by the figure below?
- One to one
- Onto
- Bijection
- Not a function
Correct Answer

A. Not a function

Explanation

The figure shown does not pass the vertical line test, meaning that there are multiple values of the independent variable (x) that correspond to the same value of the dependent variable (y). This violates the definition of a function, which states that each value of x must have a unique corresponding value of y. Therefore, the figure does not represent a function.

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1