example 1 express each relation as a table, a graph, and a mapping. then determine the domain and range. 1. {(4, 3), (-2, 2), (5, -6)} 2. {(5, -7), (-1, 4), (0, -5), (-2, 3)} example 2 identify the independent and dependent variables for each relation. 3. increasing the temperature of a compound inside a sealed container increases the pressure inside a sealed container. 4. mikes cell phone is part of a family plan. if he uses more data than his share, then there is less data available for the rest of his family. 5. julian is buying concert tickets for himself and his friends. if he buys more concert tickets, the cost is greater. 6. a store is having a sale over labor day weekend. when there are more purchases, the profits are greater. example 3 mp modeling describe what is happening in each graph. 7. the graph represents the distance the track team runs during a practice. 8. the graph represents revenues generated through an online store. practice and problem solving extra practice is on page r1. example 1 express each relation as a table, a graph, and a mapping. then determine the domain and range. 9. {(0, 0), (-3, 2), (6, 4), (-1, 1)} 10. {(5, 2), (5, 6), (3, -2), (0, -2)} 11. {(6, 1), (4, -3), (3, 2), (-1, -3)} 12. {(-1, 3), (3, -6), (-1, -8), (-3, -7)} 13. {(6, 7), (3, -2), (8, 8), (-6, 2), (2, -6)} 14. {(4, -3), (1, 3), (7, -2), (2, -2), (1, 5)} example 2 identify the independent and dependent variables for each relation. 15 the spanish classes are having a fiesta lunch. each student who attends is to bring a spanish side dish or dessert. the more students who attend, the more food there will be available. 16. the faster you drive your car, the longer it will take to come to a complete stop.

Question

Accepted Answer

### 1. For relation $\{(4,3),(-2,2),(5, - 6)\}$
# Explanation:
## Step1: Create a table
| $x$ | $y$ |
|----|----|
| $4$ | $3$ |
| $-2$ | $2$ |
| $5$ | $-6$ |
## Step2: Create a mapping
The mapping is $4
ightarrow3$, $-2
ightarrow2$, $5
ightarrow - 6$
## Step3: Determine the domain and range
The domain is the set of all $x -$values. So, domain $=\{4,-2,5\}$
The range is the set of all $y -$values. So, range $=\{3,2,-6\}$
# Answer:
Table:
| $x$ | $y$ |
|----|----|
| $4$ | $3$ |
| $-2$ | $2$ |
| $5$ | $-6$ |
Mapping: $4
ightarrow3$, $-2
ightarrow2$, $5
ightarrow - 6$
Domain: $\{4,-2,5\}$
Range: $\{3,2,-6\}$

### 2. For relation $\{(5,-7),(-1,4),(0,-5),(-2,3)\}$
# Explanation:
## Step1: Create a table
| $x$ | $y$ |
|----|----|
| $5$ | $-7$ |
| $-1$ | $4$ |
| $0$ | $-5$ |
| $-2$ | $3$ |
## Step2: Create a mapping
The mapping is $5
ightarrow - 7$, $-1
ightarrow4$, $0
ightarrow - 5$, $-2
ightarrow3$
## Step3: Determine the domain and range
The domain is the set of all $x -$values. So, domain $=\{5,-1,0,-2\}$
The range is the set of all $y -$values. So, range $=\{-7,4,-5,3\}$
# Answer:
Table:
| $x$ | $y$ |
|----|----|
| $5$ | $-7$ |
| $-1$ | $4$ |
| $0$ | $-5$ |
| $-2$ | $3$ |
Mapping: $5
ightarrow - 7$, $-1
ightarrow4$, $0
ightarrow - 5$, $-2
ightarrow3$
Domain: $\{5,-1,0,-2\}$
Range: $\{-7,4,-5,3\}$

### 3. For the relation "Increasing the temperature of a compound inside a sealed container increases the pressure inside a sealed container"
# Explanation:
The independent variable is the variable that is being changed or controlled. Here, the temperature of the compound is being changed. The dependent variable is the variable that depends on the independent - variable. Here, the pressure inside the container depends on the temperature.
# Answer:
Independent variable: Temperature of the compound
Dependent variable: Pressure inside the sealed container

### 4. For the relation "Mike's cell phone is part of a family plan. If he uses more data than his share, then there is less data available for the rest of his family"
# Explanation:
The amount of data Mike uses is the variable that he can control (or that can change). The amount of data available for the rest of the family depends on how much data Mike uses.
# Answer:
Independent variable: Amount of data Mike uses
Dependent variable: Amount of data available for the rest of the family

### 5. For the relation "Julian is buying concert tickets for himself and his friends. If he buys more concert tickets, the cost is greater"
# Explanation:
The number of concert tickets Julian buys is the variable that can be changed. The cost of the tickets depends on the number of tickets bought.
# Answer:
Independent variable: Number of concert tickets Julian buys
Dependent variable: Cost of the concert tickets

### 6. For the relation "A store is having a sale over Labor Day weekend. When there are more purchases, the profits are greater"
# Explanation:
The number of purchases is the variable that can change. The profit of the store depends on the number of purchases made.
# Answer:
Independent variable: Number of purchases
Dependent variable: Profits of the store

### 7. For the graph representing the distance the track team runs during a practice
# Explanation:
As time increases, the distance the track team runs also increases. There may be some periods where the team takes a break (flat - part of the graph), but overall, the distance is non - decreasing with time.
# Answer:
As time passes during the practice, the distance the track team runs increases. There may be intervals where the team stops running (resulting in a horizontal part of the graph), but the overall trend is that distance accumulates over time.

### 8. For the graph representing revenues generated through an online store
# Explanation:
As time passes, the revenues generated through the online store increase. There may be some fluctuations (decreases or plateaus) in the revenue over time, but the overall trend is an upward - sloping curve indicating growth in revenue.
# Answer:
As time elapses, the revenues of the online store increase. There are some fluctuations in the revenue over time, but the general trend is a growth in revenue values.

### 9. For relation $\{(0,0),(-3,2),(6,4),(-1,1)\}$
# Explanation:
## Step1: Create a table
| $x$ | $y$ |
|----|----|
| $0$ | $0$ |
| $-3$ | $2$ |
| $6$ | $4$ |
| $-1$ | $1$ |
## Step2: Create a mapping
The mapping is $0
ightarrow0$, $-3
ightarrow2$, $6
ightarrow4$, $-1
ightarrow1$
## Step3: Determine the domain and range
The domain is the set of all $x -$values. So, domain $=\{0,-3,6,-1\}$
The range is the set of all $y -$values. So, range $=\{0,2,4,1\}$
# Answer:
Table:
| $x$ | $y$ |
|----|----|
| $0$ | $0$ |
| $-3$ | $2$ |
| $6$ | $4$ |
| $-1$ | $1$ |
Mapping: $0
ightarrow0$, $-3
ightarrow2$, $6
ightarrow4$, $-1
ightarrow1$
Domain: $\{0,-3,6,-1\}$
Range: $\{0,2,4,1\}$

### 10. For relation $\{(5,2),(5,6),(3,-2),(0,-2)\}$
# Explanation:
## Step1: Create a table
| $x$ | $y$ |
|----|----|
| $5$ | $2$ |
| $5$ | $6$ |
| $3$ | $-2$ |
| $0$ | $-2$ |
## Step2: Create a mapping
The mapping is $5
ightarrow2$, $5
ightarrow6$, $3
ightarrow - 2$, $0
ightarrow - 2$
## Step3: Determine the domain and range
The domain is the set of all $x -$values. So, domain $=\{5,3,0\}$
The range is the set of all $y -$values. So, range $=\{2,6,-2\}$
# Answer:
Table:
| $x$ | $y$ |
|----|----|
| $5$ | $2$ |
| $5$ | $6$ |
| $3$ | $-2$ |
| $0$ | $-2$ |
Mapping: $5
ightarrow2$, $5
ightarrow6$, $3
ightarrow - 2$, $0
ightarrow - 2$
Domain: $\{5,3,0\}$
Range: $\{2,6,-2\}$

### 11. For relation $\{(6,1),(4,-3),(3,2),(-1,-3)\}$
# Explanation:
## Step1: Create a table
| $x$ | $y$ |
|----|----|
| $6$ | $1$ |
| $4$ | $-3$ |
| $3$ | $2$ |
| $-1$ | $-3$ |
## Step2: Create a mapping
The mapping is $6
ightarrow1$, $4
ightarrow - 3$, $3
ightarrow2$, $-1
ightarrow - 3$
## Step3: Determine the domain and range
The domain is the set of all $x -$values. So, domain $=\{6,4,3,-1\}$
The range is the set of all $y -$values. So, range $=\{1,-3,2\}$
# Answer:
Table:
| $x$ | $y$ |
|----|----|
| $6$ | $1$ |
| $4$ | $-3$ |
| $3$ | $2$ |
| $-1$ | $-3$ |
Mapping: $6
ightarrow1$, $4
ightarrow - 3$, $3
ightarrow2$, $-1
ightarrow - 3$
Domain: $\{6,4,3,-1\}$
Range: $\{1,-3,2\}$

### 12. For relation $\{(-1,3),(3,-6),(-1,-8),(-3,-7)\}$
# Explanation:
## Step1: Create a table
| $x$ | $y$ |
|----|----|
| $-1$ | $3$ |
| $3$ | $-6$ |
| $-1$ | $-8$ |
| $-3$ | $-7$ |
## Step2: Create a mapping
The mapping is $-1
ightarrow3$, $-1
ightarrow - 8$, $3
ightarrow - 6$, $-3
ightarrow - 7$
## Step3: Determine the domain and range
The domain is the set of all $x -$values. So, domain $=\{-1,3,-3\}$
The range is the set of all $y -$values. So, range $=\{3,-6,-8,-7\}$
# Answer:
Table:
| $x$ | $y$ |
|----|----|
| $-1$ | $3$ |
| $3$ | $-6$ |
| $-1$ | $-8$ |
| $-3$ | $-7$ |
Mapping: $-1
ightarrow3$, $-1
ightarrow - 8$, $3
ightarrow - 6$, $-3
ightarrow - 7$
Domain: $\{-1,3,-3\}$
Range: $\{3,-6,-8,-7\}$

### 13. For relation $\{(6,7),(3,-2),(8,8),(-6,2),(2,-6)\}$
# Explanation:
## Step1: Create a table
| $x$ | $y$ |
|----|----|
| $6$ | $7$ |
| $3$ | $-2$ |
| $8$ | $8$ |
| $-6$ | $2$ |
| $2$ | $-6$ |
## Step2: Create a mapping
The mapping is $6
ightarrow7$, $3
ightarrow - 2$, $8
ightarrow8$, $-6
ightarrow2$, $2
ightarrow - 6$
## Step3: Determine the domain and range
The domain is the set of all $x -$values. So, domain $=\{6,3,8,-6,2\}$
The range is the set of all $y -$values. So, range $=\{7,-2,8,2,-6\}$
# Answer:
Table:
| $x$ | $y$ |
|----|----|
| $6$ | $7$ |
| $3$ | $-2$ |
| $8$ | $8$ |
| $-6$ | $2$ |
| $2$ | $-6$ |
Mapping: $6
ightarrow7$, $3
ightarrow - 2$, $8
ightarrow8$, $-6
ightarrow2$, $2
ightarrow - 6$
Domain: $\{6,3,8,-6,2\}$
Range: $\{7,-2,8,2,-6\}$

### 14. For relation $\{(4,-3),(1,3),(7,-2),(2,-2),(1,5)\}$
# Explanation:
## Step1: Create a table
| $x$ | $y$ |
|----|----|
| $4$ | $-3$ |
| $1$ | $3$ |
| $7$ | $-2$ |
| $2$ | $-2$ |
| $1$ | $5$ |
## Step2: Create a mapping
The mapping is $4
ightarrow - 3$, $1
ightarrow3$, $1
ightarrow5$, $7
ightarrow - 2$, $2
ightarrow - 2$
## Step3: Determine the domain and range
The domain is the set of all $x -$values. So, domain $=\{4,1,7,2\}$
The range is the set of all $y -$values. So, range $=\{-3,3,5,-2\}$
# Answer:
Table:
| $x$ | $y$ |
|----|----|
| $4$ | $-3$ |
| $1$ | $3$ |
| $7$ | $-2$ |
| $2$ | $-2$ |
| $1$ | $5$ |
Mapping: $4
ightarrow - 3$, $1
ightarrow3$, $1
ightarrow5$, $7
ightarrow - 2$, $2
ightarrow - 2$
Domain: $\{4,1,7,2\}$
Range: $\{-3,3,5,-2\}$

### 15. For the relation "The Spanish classes are having a fiesta lunch. Each student who attends is to bring a Spanish side - dish or dessert. The more students who attend, the more food there will be available"
# Explanation:
The number of students who attend the fiesta lunch is the variable that can change. The amount of food available depends on the number of students who attend.
# Answer:
Independent variable: Number of students who attend the fiesta lunch
Dependent variable: Amount of food available

### 16. For the relation "The faster you drive your car, the longer it will take to come to a complete stop"
# Explanation:
The speed at which you drive the car is the variable that can be changed. The stopping time of the car depends on the speed of the car.
# Answer:
Independent variable: Speed of the car
Dependent variable: Stopping time of the car

\(x\)	\(y\)
\(-2\)	\(2\)
\(5\)	\(-6\)

\(x\)	\(y\)
\(-1\)	\(4\)
\(0\)	\(-5\)
\(-2\)	\(3\)

\(x\)	\(y\)
\(-2\)	\(2\)
\(5\)	\(-6\)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

1. For relation \(\{(4,3),(-2,2),(5, - 6)\}\)

Step1: Create a table

Step2: Create a mapping

Step3: Determine the domain and range

Step1: Create a table

Step2: Create a mapping

Step3: Determine the domain and range

Answer:

2. For relation \(\{(5,-7),(-1,4),(0,-5),(-2,3)\}\)