Answer :
Let's analyze the given table and determine what observations can be made. Here's the table for reference:
[tex]\[ \begin{tabular}{|c|c|} \hline Gallons, $g$ & Liters, $l$ \\ \hline 1 & 3.79 \\ \hline 2 & 7.58 \\ \hline 3 & 11.37 \\ \hline 4 & 15.16 \\ \hline 5 & 18.95 \\ \hline 6 & 22.74 \\ \hline \end{tabular} \][/tex]
### Step-by-Step Solution:
1. Independent Variable:
- The independent variable is typically the variable that you control or decide. In this table, we choose different values for gallons ([tex]$g$[/tex]) and measure the corresponding liters ([tex]$l$[/tex]). Hence, the independent variable is the number of gallons.
2. Liters as a Function of Gallons:
- In the table, for each value of gallons ([tex]$g$[/tex]), there is a corresponding single value for liters ([tex]$l$[/tex]). This implies that liters can be described as a function of gallons. This makes sense because for every input (gallons), there is one output (liters).
3. Equation Representation:
- Upon examining each row of the table, we can observe that the value of liters ([tex]$l$[/tex]) is calculated as [tex]$l = 3.79g$[/tex]. This equation accurately represents the relationship between gallons and liters as seen in the table data.
4. Increase Relationship:
- Observing the table, as the number of gallons increases from 1 to 6, the number of liters also increases accordingly. This means there is a direct relationship where an increase in gallons results in an increase in liters.
5. Function Definition:
- In a function, each input must correspond to exactly one output. Evaluating the table, for each gallon value (input), there is exactly one unique liter value (output). Therefore, this relationship qualifies as a function.
### Final Observations:
Based on the analysis above, the valid observations from the table are:
- 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.
These observations provide a comprehensive understanding of the relationship described in the table.
[tex]\[ \begin{tabular}{|c|c|} \hline Gallons, $g$ & Liters, $l$ \\ \hline 1 & 3.79 \\ \hline 2 & 7.58 \\ \hline 3 & 11.37 \\ \hline 4 & 15.16 \\ \hline 5 & 18.95 \\ \hline 6 & 22.74 \\ \hline \end{tabular} \][/tex]
### Step-by-Step Solution:
1. Independent Variable:
- The independent variable is typically the variable that you control or decide. In this table, we choose different values for gallons ([tex]$g$[/tex]) and measure the corresponding liters ([tex]$l$[/tex]). Hence, the independent variable is the number of gallons.
2. Liters as a Function of Gallons:
- In the table, for each value of gallons ([tex]$g$[/tex]), there is a corresponding single value for liters ([tex]$l$[/tex]). This implies that liters can be described as a function of gallons. This makes sense because for every input (gallons), there is one output (liters).
3. Equation Representation:
- Upon examining each row of the table, we can observe that the value of liters ([tex]$l$[/tex]) is calculated as [tex]$l = 3.79g$[/tex]. This equation accurately represents the relationship between gallons and liters as seen in the table data.
4. Increase Relationship:
- Observing the table, as the number of gallons increases from 1 to 6, the number of liters also increases accordingly. This means there is a direct relationship where an increase in gallons results in an increase in liters.
5. Function Definition:
- In a function, each input must correspond to exactly one output. Evaluating the table, for each gallon value (input), there is exactly one unique liter value (output). Therefore, this relationship qualifies as a function.
### Final Observations:
Based on the analysis above, the valid observations from the table are:
- 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.
These observations provide a comprehensive understanding of the relationship described in the table.
