Answer :
To analyze the given table and determine what can be concluded, let's carefully consider each statement provided:
1. The independent variable is the number of gallons.
- In the context of this table, the number of gallons ([tex]$g$[/tex]) is the independent variable, as it is what we are manipulating to observe the corresponding values in liters ([tex]$l$[/tex]). This matches our conventional understanding of independent and dependent variables in functional relationships.
2. Liters is a function of Gallons.
- A function is defined as a relationship where each input (in this case, each number of gallons) corresponds to exactly one output (liters). According to the table, each value of gallons has a specific corresponding value in liters, affirming that liters is indeed a function of gallons.
3. The equation [tex]$l = 3.79g$[/tex] represents the table.
- The data from the table can be cross-checked with the equation [tex]$l = 3.79g$[/tex]. Each value of gallons multiplied by 3.79 yields the corresponding number of liters:
- For [tex]\( g = 1 \)[/tex], [tex]\( l = 3.79 \times 1 = 3.79 \)[/tex]
- For [tex]\( g = 2 \)[/tex], [tex]\( l = 3.79 \times 2 = 7.58 \)[/tex]
- For [tex]\( g = 3 \)[/tex], [tex]\( l = 3.79 \times 3 = 11.37 \)[/tex]
- For [tex]\( g = 4 \)[/tex], [tex]\( l = 3.79 \times 4 = 15.16 \)[/tex]
- For [tex]\( g = 5 \)[/tex], [tex]\( l = 3.79 \times 5 = 18.95 \)[/tex]
- For [tex]\( g = 6 \)[/tex], [tex]\( l = 3.79 \times 6 = 22.74 \)[/tex]
- Since these computed values match the table, the equation [tex]$l = 3.79g$[/tex] accurately represents the relationship between gallons and liters shown in the table.
4. As the number of gallons increases, the number of liters increases.
- Observing the table, as the number of gallons increases from 1 to 6, the corresponding number of liters also increases proportionally. Thus, this relationship indicates a direct proportionality between gallons and liters.
5. This is a function because every input has exactly one output.
- Referring to the definition of a function, where each input must have exactly one output, the table satisfies this requirement. Each value of gallons corresponds to one and only one value in liters, confirming that this relationship is indeed a function.
Based on the analysis, all the given statements correctly describe the relationship presented in the table. Therefore, we can conclude:
- The independent variable is the number of gallons.
- Liters is a function of Gallons.
- The equation [tex]\( l = 3.79g \)[/tex] represents the table.
- As the number of gallons increases, the number of liters increases.
- This is a function because every input has exactly one output.
1. The independent variable is the number of gallons.
- In the context of this table, the number of gallons ([tex]$g$[/tex]) is the independent variable, as it is what we are manipulating to observe the corresponding values in liters ([tex]$l$[/tex]). This matches our conventional understanding of independent and dependent variables in functional relationships.
2. Liters is a function of Gallons.
- A function is defined as a relationship where each input (in this case, each number of gallons) corresponds to exactly one output (liters). According to the table, each value of gallons has a specific corresponding value in liters, affirming that liters is indeed a function of gallons.
3. The equation [tex]$l = 3.79g$[/tex] represents the table.
- The data from the table can be cross-checked with the equation [tex]$l = 3.79g$[/tex]. Each value of gallons multiplied by 3.79 yields the corresponding number of liters:
- For [tex]\( g = 1 \)[/tex], [tex]\( l = 3.79 \times 1 = 3.79 \)[/tex]
- For [tex]\( g = 2 \)[/tex], [tex]\( l = 3.79 \times 2 = 7.58 \)[/tex]
- For [tex]\( g = 3 \)[/tex], [tex]\( l = 3.79 \times 3 = 11.37 \)[/tex]
- For [tex]\( g = 4 \)[/tex], [tex]\( l = 3.79 \times 4 = 15.16 \)[/tex]
- For [tex]\( g = 5 \)[/tex], [tex]\( l = 3.79 \times 5 = 18.95 \)[/tex]
- For [tex]\( g = 6 \)[/tex], [tex]\( l = 3.79 \times 6 = 22.74 \)[/tex]
- Since these computed values match the table, the equation [tex]$l = 3.79g$[/tex] accurately represents the relationship between gallons and liters shown in the table.
4. As the number of gallons increases, the number of liters increases.
- Observing the table, as the number of gallons increases from 1 to 6, the corresponding number of liters also increases proportionally. Thus, this relationship indicates a direct proportionality between gallons and liters.
5. This is a function because every input has exactly one output.
- Referring to the definition of a function, where each input must have exactly one output, the table satisfies this requirement. Each value of gallons corresponds to one and only one value in liters, confirming that this relationship is indeed a function.
Based on the analysis, all the given statements correctly describe the relationship presented in the table. Therefore, we can conclude:
- The independent variable is the number of gallons.
- Liters is a function of Gallons.
- The equation [tex]\( l = 3.79g \)[/tex] represents the table.
- As the number of gallons increases, the number of liters increases.
- This is a function because every input has exactly one output.
