For the following exercises, (a) determine the domain and the range of each relation, and (b) state whether the relation is a function. 1. x y x y -3 9 1 1 2 4 2 4 -1 1 3 9 0 0

Question

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Answer 1

Textbook Question

Chapter 1.1, Problem 1E

For the following exercises, (a) determine the domain and the range of each relation, and (b) state whether the relation is a function.

1.

x	y	x	y
-3	9	1	1
2	4	2	4
-1	1	3	9
0	0

a.

Expert Solution

To determine

The domain and the range of given relation

Answer to Problem 1E

The domain is D∈{−3,−2,−1,0,1,2,3} and the range is R∈{0,1,4,9}

Explanation of Solution

Given:

We are given with a Table as below:

Calculus Volume 1, Chapter 1.1, Problem 1E , additional homework tip 1

Concept Used:

A relation is defined as the set of ordered pairs. A function consists of three important parts, the input values, the output values and a rule or a set of rules which defines the relation between input and output.

Here the set of input is known as Domain whereas the set of output is known as the Range.

Calculation:

Using the concept that a relation is defined as the set of ordered pairs and a function consists of three important parts, the input values, the output values and a rule or a set of rules which defines the relation between input and output. Here the set of input is known as Domain whereas the set of output is known as the Range.

So we can say the Domain is D∈{−3,−2,−1,0,1,2,3}

The range of the relation is R∈{0,1,4,9}

Conclusion:

The domain and the range of given relation is D∈{−3,−2,−1,0,1,2,3} and R∈{0,1,4,9} respectively.

b.

Expert Solution

To determine

State whether the relation is a function.

Answer to Problem 1E

The given relation is a function.

Explanation of Solution

Given:

We are given with a Table as below:

Calculus Volume 1, Chapter 1.1, Problem 1E , additional homework tip 2

Concept Used:

A function relates every elements of domain to exactly one element in the range.

Calculation:

Using the concept-A function relates every elements of domain to exactly one element in the range.

We can observe from the given table that every elements of domain relates to exactly one element in the range.

Hence the given relation is a function.

Conclusion:

The given relation is a function.

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A 12-inch bar that is clamped at both ends is to be subjected to an increasing amount of stress until it snaps. Let Y = the distance from the left end at which the break occurs. Suppose Y has the following pdf. f(y) = { (a) Compute the cdf of Y. F(y) = 0 0 y -옴) 0 ≤ y ≤ 12 1- 12 y 12 Graph the cdf of Y. F(y) 1.0 0.8 0.6 0.4 0.2 y 2 6 8 10 12 F(y) F(y) F(y) 1.01 1.0ㅏ 1.0 0.8 0.6 0.4 0.2 0.8 0.8 0.6 0.4 ཨཱུ སྦེ 0.6 0.4 0.2 2 4 6 8 10 12 (b) Compute P(Y ≤ 5), P(Y > 6), and P(5 ≤ y ≤ 6). (Round your answers to three decimal places.) P(Y ≤ 5) = P(Y > 6) = P(5 ≤ y ≤ 6) = (c) Compute E(Y), E(y²), and V(Y). E(Y) = in E(Y2) v(x) = in 2 2 2 4 6 8 10 12 y 2 4 6 8 10 12

Answer 2

Textbook Question

Chapter 1.1, Problem 1E

For the following exercises, (a) determine the domain and the range of each relation, and (b) state whether the relation is a function.

1.

x	y	x	y
-3	9	1	1
2	4	2	4
-1	1	3	9
0	0

a.

Expert Solution

To determine

The domain and the range of given relation

Answer to Problem 1E

The domain is D∈{−3,−2,−1,0,1,2,3} and the range is R∈{0,1,4,9}

Explanation of Solution

Given:

We are given with a Table as below:

Calculus Volume 1, Chapter 1.1, Problem 1E , additional homework tip 1

Concept Used:

A relation is defined as the set of ordered pairs. A function consists of three important parts, the input values, the output values and a rule or a set of rules which defines the relation between input and output.

Here the set of input is known as Domain whereas the set of output is known as the Range.

Calculation:

Using the concept that a relation is defined as the set of ordered pairs and a function consists of three important parts, the input values, the output values and a rule or a set of rules which defines the relation between input and output. Here the set of input is known as Domain whereas the set of output is known as the Range.

So we can say the Domain is D∈{−3,−2,−1,0,1,2,3}

The range of the relation is R∈{0,1,4,9}

Conclusion:

The domain and the range of given relation is D∈{−3,−2,−1,0,1,2,3} and R∈{0,1,4,9} respectively.

b.

Expert Solution

To determine

State whether the relation is a function.

Answer to Problem 1E

The given relation is a function.

Explanation of Solution

Given:

We are given with a Table as below:

Calculus Volume 1, Chapter 1.1, Problem 1E , additional homework tip 2

Concept Used:

A function relates every elements of domain to exactly one element in the range.

Calculation:

Using the concept-A function relates every elements of domain to exactly one element in the range.

We can observe from the given table that every elements of domain relates to exactly one element in the range.

Hence the given relation is a function.

Conclusion:

The given relation is a function.

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Answer 3

Textbook Question

Chapter 1.1, Problem 1E

For the following exercises, (a) determine the domain and the range of each relation, and (b) state whether the relation is a function.

1.

x	y	x	y
-3	9	1	1
2	4	2	4
-1	1	3	9
0	0

a.

Expert Solution

To determine

The domain and the range of given relation

Answer to Problem 1E

The domain is D∈{−3,−2,−1,0,1,2,3} and the range is R∈{0,1,4,9}

Explanation of Solution

Given:

We are given with a Table as below:

Calculus Volume 1, Chapter 1.1, Problem 1E , additional homework tip 1

Concept Used:

A relation is defined as the set of ordered pairs. A function consists of three important parts, the input values, the output values and a rule or a set of rules which defines the relation between input and output.

Here the set of input is known as Domain whereas the set of output is known as the Range.

Calculation:

Using the concept that a relation is defined as the set of ordered pairs and a function consists of three important parts, the input values, the output values and a rule or a set of rules which defines the relation between input and output. Here the set of input is known as Domain whereas the set of output is known as the Range.

So we can say the Domain is D∈{−3,−2,−1,0,1,2,3}

The range of the relation is R∈{0,1,4,9}

Conclusion:

The domain and the range of given relation is D∈{−3,−2,−1,0,1,2,3} and R∈{0,1,4,9} respectively.

b.

Expert Solution

To determine

State whether the relation is a function.

Answer to Problem 1E

The given relation is a function.

Explanation of Solution

Given:

We are given with a Table as below:

Calculus Volume 1, Chapter 1.1, Problem 1E , additional homework tip 2

Concept Used:

A function relates every elements of domain to exactly one element in the range.

Calculation:

Using the concept-A function relates every elements of domain to exactly one element in the range.

We can observe from the given table that every elements of domain relates to exactly one element in the range.

Hence the given relation is a function.

Conclusion:

The given relation is a function.

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Answer 4

Textbook Question

Chapter 1.1, Problem 1E

For the following exercises, (a) determine the domain and the range of each relation, and (b) state whether the relation is a function.

1.

x	y	x	y
-3	9	1	1
2	4	2	4
-1	1	3	9
0	0

a.

Expert Solution

To determine

The domain and the range of given relation

Answer to Problem 1E

The domain is D∈{−3,−2,−1,0,1,2,3} and the range is R∈{0,1,4,9}

Explanation of Solution

Given:

We are given with a Table as below:

Calculus Volume 1, Chapter 1.1, Problem 1E , additional homework tip 1

Concept Used:

A relation is defined as the set of ordered pairs. A function consists of three important parts, the input values, the output values and a rule or a set of rules which defines the relation between input and output.

Here the set of input is known as Domain whereas the set of output is known as the Range.

Calculation:

Using the concept that a relation is defined as the set of ordered pairs and a function consists of three important parts, the input values, the output values and a rule or a set of rules which defines the relation between input and output. Here the set of input is known as Domain whereas the set of output is known as the Range.

So we can say the Domain is D∈{−3,−2,−1,0,1,2,3}

The range of the relation is R∈{0,1,4,9}

Conclusion:

The domain and the range of given relation is D∈{−3,−2,−1,0,1,2,3} and R∈{0,1,4,9} respectively.

b.

Expert Solution

To determine

State whether the relation is a function.

Answer to Problem 1E

The given relation is a function.

Explanation of Solution

Given:

We are given with a Table as below:

Calculus Volume 1, Chapter 1.1, Problem 1E , additional homework tip 2

Concept Used:

A function relates every elements of domain to exactly one element in the range.

Calculation:

Using the concept-A function relates every elements of domain to exactly one element in the range.

We can observe from the given table that every elements of domain relates to exactly one element in the range.

Hence the given relation is a function.

Conclusion:

The given relation is a function.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

a.

Expert Solution

To determine

The domain and the range of given relation

Answer to Problem 1E

The domain is D∈{−3,−2,−1,0,1,2,3} and the range is R∈{0,1,4,9}

Explanation of Solution

Given:

We are given with a Table as below:

Calculus Volume 1, Chapter 1.1, Problem 1E , additional homework tip 1

Concept Used:

A relation is defined as the set of ordered pairs. A function consists of three important parts, the input values, the output values and a rule or a set of rules which defines the relation between input and output.

Here the set of input is known as Domain whereas the set of output is known as the Range.

Calculation:

Using the concept that a relation is defined as the set of ordered pairs and a function consists of three important parts, the input values, the output values and a rule or a set of rules which defines the relation between input and output. Here the set of input is known as Domain whereas the set of output is known as the Range.

So we can say the Domain is D∈{−3,−2,−1,0,1,2,3}

The range of the relation is R∈{0,1,4,9}

Conclusion:

The domain and the range of given relation is D∈{−3,−2,−1,0,1,2,3} and R∈{0,1,4,9} respectively.

b.

Expert Solution

To determine

State whether the relation is a function.

Answer to Problem 1E

The given relation is a function.

Explanation of Solution

Given:

We are given with a Table as below:

Calculus Volume 1, Chapter 1.1, Problem 1E , additional homework tip 2

Concept Used:

A function relates every elements of domain to exactly one element in the range.

Calculation:

Using the concept-A function relates every elements of domain to exactly one element in the range.

We can observe from the given table that every elements of domain relates to exactly one element in the range.

Hence the given relation is a function.

Conclusion:

The given relation is a function.

Answer 8

a.

Expert Solution

To determine

The domain and the range of given relation

Answer to Problem 1E

The domain is D∈{−3,−2,−1,0,1,2,3} and the range is R∈{0,1,4,9}

Explanation of Solution

Given:

We are given with a Table as below:

Calculus Volume 1, Chapter 1.1, Problem 1E , additional homework tip 1

Concept Used:

A relation is defined as the set of ordered pairs. A function consists of three important parts, the input values, the output values and a rule or a set of rules which defines the relation between input and output.

Here the set of input is known as Domain whereas the set of output is known as the Range.

Calculation:

Using the concept that a relation is defined as the set of ordered pairs and a function consists of three important parts, the input values, the output values and a rule or a set of rules which defines the relation between input and output. Here the set of input is known as Domain whereas the set of output is known as the Range.

So we can say the Domain is D∈{−3,−2,−1,0,1,2,3}

The range of the relation is R∈{0,1,4,9}

Conclusion:

The domain and the range of given relation is D∈{−3,−2,−1,0,1,2,3} and R∈{0,1,4,9} respectively.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

The domain and the range of given relation

Answer 13

Answer to Problem 1E

The domain is D∈{−3,−2,−1,0,1,2,3} and the range is R∈{0,1,4,9}

Answer 14

Explanation of Solution

Given:

We are given with a Table as below:

Calculus Volume 1, Chapter 1.1, Problem 1E , additional homework tip 1

Concept Used:

A relation is defined as the set of ordered pairs. A function consists of three important parts, the input values, the output values and a rule or a set of rules which defines the relation between input and output.

Here the set of input is known as Domain whereas the set of output is known as the Range.

Calculation:

Using the concept that a relation is defined as the set of ordered pairs and a function consists of three important parts, the input values, the output values and a rule or a set of rules which defines the relation between input and output. Here the set of input is known as Domain whereas the set of output is known as the Range.

So we can say the Domain is D∈{−3,−2,−1,0,1,2,3}

The range of the relation is R∈{0,1,4,9}

Conclusion:

The domain and the range of given relation is D∈{−3,−2,−1,0,1,2,3} and R∈{0,1,4,9} respectively.

Answer 15

b.

Expert Solution

To determine

State whether the relation is a function.

Answer to Problem 1E

The given relation is a function.

Explanation of Solution

Given:

We are given with a Table as below:

Calculus Volume 1, Chapter 1.1, Problem 1E , additional homework tip 2

Concept Used:

A function relates every elements of domain to exactly one element in the range.

Calculation:

Using the concept-A function relates every elements of domain to exactly one element in the range.

We can observe from the given table that every elements of domain relates to exactly one element in the range.

Hence the given relation is a function.

Conclusion:

The given relation is a function.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

State whether the relation is a function.

Answer 20

Answer to Problem 1E

The given relation is a function.

Answer 21

Explanation of Solution

Given:

We are given with a Table as below:

Calculus Volume 1, Chapter 1.1, Problem 1E , additional homework tip 2

Concept Used:

A function relates every elements of domain to exactly one element in the range.

Calculation:

Using the concept-A function relates every elements of domain to exactly one element in the range.

We can observe from the given table that every elements of domain relates to exactly one element in the range.

Hence the given relation is a function.

Conclusion:

The given relation is a function.

Answer 22

For the following exercises, (a) determine the domain and the range of each relation, and (b) state whether the relation is a function. 1. x y x y -3 9 1 1 2 4 2 4 -1 1 3 9 0 0

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Answer to Problem 1E

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Answer to Problem 1E

Explanation of Solution

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