## Envision Math Grade 8 Volume 1 Chapter 3 Use Functions To Model Relationships

**Page 159 Exercise 1 Answer**

A relation is said to be a function if it relates one value of its domain to one value of its range.

Also, is one input has only one output, the relation is a function.

Jesse plan is to sell 50 tickets but it will not fulfill the requirement of $500 as different amount of tickets have different values.

In case of Alexis plan, the target will be achieved if each person sells the tickets of $50 .

Alexis plan would be recommended to fulfill the requirement.

**Page 159 Exercise 1 Answer**

A relation is said to be a function if it relates one value of its domain to one value of its range.

Also, is one input has only one output, the relation is a function.

Jesse plan is to sell 50 tickets per head which will get them approximately $400 from each person.

In case of Alexis plan, a person should sell the tickets of $50 and they will be able to collect $500 from 10 persons.

Plans are different as they have different strategies to collect the amount whereas the similarity is that they have to collect equal amount, i.e. $500 .

**Page 160 Exercise 1 Answer**

A relation is said to be a function if it relates one value of its domain to one value of its range.

Also, is one input has only one output, the relation is a function.

Different weights of the boxes have different cost of shipping ,i.e. the cost of shipping has unique values.

Yes. There is a relation between weight of the box and the cost to ship the box.

**Page 160 Exercise 1 Answer**

The given points are (4,24),(5,35),(8,24),(2,20),(9,27)

Find: complete arrow diagram and explain

The completed arrow diagram is:

Each side length has one line connected to it. So, area is a function of side length.

The required arrow diagram is:

Yes. The area of the brochure is a function of the side length.

**Page 161 Exercise 3 Answer**

A relation is said to be a function if it relates one value of its domain to one value of its range.

Also, is one input has only one output, the relation is a function.

Each cost of parking has different timings of parking by which it can be determined that for how much time the vehicle was parked according to the amount paid.

Heather is correct because this relation is a function.

**Page 160 Exercise 1 Answer**

A relation is said to be a function if it relates one value of its domain to one value of its range.

Also, is one input has only one output, the relation is a function.

If there are two outputs of the input 24, then it is not a function.

The given relation is not a function because one input has two output.

**Page 162 Exercise 2 Answer**

Given

Use different representation of a relation to determine whether the relation is a function?

We can use diagrams and tables to determine whether relation is function.

When we use diagrams than we simply have to look if there are multiple arrows connected to the same output.

When, we use tables again we simply have to look if the given inputs always give different outputs or the relation is a not function.

We use Diagram and table representations of a relation to determine whether the relation is a function.

**Page 162 Exercise 3 Answer**

Given

The relation is always a function and function is always a relation?

A relation does not always have to be a function, but a function is always a relation.

When we have some relation we can have multiple inputs give out different outputs, but the functions always give different outputs for every single inputs.

A relation does not always a function, but a function is always a relation.

**Page 162 Exercise 5 Answer**

Given

Inputs are 3,4,1,5,2

Outputs are 4,6,2,8,5

Find the relation is function or not?

We can see from the table each of the inputs corresponds to exactly one output. This means that given relation is a function.

This relation is a function.

**Page 162 Exercise 6 Answer**

Given

Inputs are 3,4,1,5,2,6

Outputs are 16,25,9,36,4,1

Find the relation is function or not?

We can see from the table each of the inputs corresponds to exactly one output. This means that given relation is a function.

There is 6 different x- coordinates with 6 different corresponding y- coordinates.

This relation is a function. Because for every input exactly one output.

**Page 163 Exercise 7 Answer**

Given

Inputs are 1,2,3,4,5

Outputs are 19,23,23,29,31

Find the relation is function or not?

Here we are going to show how to make an arrow diagram.

1 → 19

2 → 23

3 → 23

4 → 29

5 → 31

Note that we put these values into a diagrams and in the right diagram with outputs we are going to have only 1 value 23.

Arrow diagram:

1 → 19

2 → 23

3 → 23

4 → 29

5 → 31

Given

Inputs are 1,2,3,4,5

Outputs are 19,23,23,29,31

Find the relation is function or not?

Here we are going to show how to make an arrow diagram.

1 → 19

2 → 23

3 → 23

4 → 29

5 → 31

A relation is an input if each input corresponds to only input.

The input 1 only corresponds to 19, 2 only corresponds to 23, 3 only corresponds to 23, 4 only corresponds to 29, 5 only corresponds to 31.

Therefore, the relation is a function. Each input corresponds to only one output.

Note that two inputs have the same output but this has no effect on whether it is a function. Repeating outputs do not determine if relation is a function, only repeating inputs determine if it is a function.

The relation is a function since each input corresponds to only one output.

**Page 163 Exercise 8 Answer**

Given

Inputs are -2,-7,-3,3,-9,-6

Outputs are 2,1,9,4,5,8

Find the relation is function or not?

Given relation is a function because there is exactly one input corresponding to one output.

The relation is a function because there is exactly one input corresponding to one output.

**Page 163 Exercise 10 Answer**

Given

Inputs are 0,5,10,15,20,25

Outputs are 15,20,50,80,100,100

Find the relation is function or not?

Given relation is not a function because there is two different inputs corresponding to same output.

The input 20 and 25 corresponds to the same output 100.

The relation is not a function .

**Page 163 Exercise 11 Answer**

Given

Inputs are 3,4,5,6,7,8

Outputs are 726,759,749,792,804,835

Find the relation is function or not?

Given relation is a function because there is exactly one inputs corresponding to exactly one output.

The relation is a function .

**Page 164 Exercise 13 Answer**

Given

Inputs are 3,7,15,16

Outputs are 6,14,6,14

Find the relation is function or not?

Here we are going to show how to make an arrow diagram.

3 → 6

7 → 14

15 → 6

16 → 14

Note that we put these values into a diagrams and in the right diagram with outputs we are going to have only one value 14 and 6.

Arrow diagram of P:

3 → 6

7 → 14

15 → 6

16 → 14

Given

Inputs are 6,6,14,14

Outputs are 7,16,3,15

Find the relation is function or not?

Here we are going to show how to make an arrow diagram.

6 → 7

6 → 16

14 → 3

14 → 15

Note that we put these values into a diagrams and in the right diagram with outputs we are going to have only 1 value 6 and 14.

Arrow diagram:

6 → 7

6 → 16

14 → 3

14 → 15

Given

Inputs are 6,6,14,14

Outputs are 7,16,3,15

Find the relation is function or not?

6 → 7 3 → 6

6 → 16 7 → 14

14 → 3 15 → 6

14 → 15 16 → 14

Neither of these two relations are functions because for a relation to be a function, each input must correspond to exactly one output.

Neither of two given relations are functions.

**Page 164 Exercise 14 Answer**

Given

Inputs are 1,6,12,18

Outputs are 2,12,24,36

Find the relation is function or not?

Here we are going to show how to make an arrow diagram.

1 → 2

6 → 12

12 → 24

18 → 36

If we look at the ordered pairs, than we can simply see that there is exactly one input of number 12 and on the diagram we can see that he drew 2 lines from the number 12 in inputs. This means that the mostly likely swapped x-coordinate with y-coordinate in one of the ordered pairs.

He most likely swapped x-coordinate with y-coordinate in one of the ordered pairs.

**Page 164 Exercise 15 Answer**

Given

Inputs are 49,61,10,76,23

Outputs are 13,36,27,52,52

Find the relation is function or not?

When we have to write ordered pairs from the diagram than we simply write the inputs which are in the left diagram as x-coordinate and the corresponding outputs as y-coordinate.

(49,13),(61,36),(10,27),(76,52),(23,52)

Given relation is a function because for it to be a function each input must correspond to exactly one output.

When we have to write ordered pairs from the diagram than we simply write the inputs which are in the left diagram as x-coordinate and the corresponding outputs as y-coordinate.

(49,13),(61,36),(10,27),(76,52),(23,52)

Given relation is a function.