Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To determine the range of the function representing the amount of water remaining in Raj's bathtub, we need to examine the given table and understand how the values change over time. The table indicates the following values:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 0 & 40 \\ \hline 0.5 & 39.25 \\ \hline 1 & 38.5 \\ \hline 1.5 & 37.75 \\ \hline \end{array} \][/tex]
Here, [tex]\(x\)[/tex] represents the time in minutes, and [tex]\(y\)[/tex] represents the amount of water remaining in the bathtub in gallons. From the table, we observe how the water level decreases with time.
- At [tex]\(x = 0\)[/tex], the water level [tex]\(y\)[/tex] is 40 gallons.
- At [tex]\(x = 0.5\)[/tex] minutes, the water level [tex]\(y\)[/tex] is 39.25 gallons.
- At [tex]\(x = 1\)[/tex] minute, the water level [tex]\(y\)[/tex] is 38.5 gallons.
- At [tex]\(x = 1.5\)[/tex] minutes, the water level [tex]\(y\)[/tex] is 37.75 gallons.
To determine the range of this function, we need to identify the minimum and maximum values of [tex]\(y\)[/tex] from the table.
- The minimum value of [tex]\(y\)[/tex] in the given table is 37.75 gallons.
- The maximum value of [tex]\(y\)[/tex] in the given table is 40 gallons.
The range of the function is therefore all real numbers [tex]\(y\)[/tex] such that [tex]\(37.75 \leq y \leq 40\)[/tex].
Thus, the correct answer is:
all real numbers such that [tex]\(37.75 \leq y \leq 40\)[/tex].
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 0 & 40 \\ \hline 0.5 & 39.25 \\ \hline 1 & 38.5 \\ \hline 1.5 & 37.75 \\ \hline \end{array} \][/tex]
Here, [tex]\(x\)[/tex] represents the time in minutes, and [tex]\(y\)[/tex] represents the amount of water remaining in the bathtub in gallons. From the table, we observe how the water level decreases with time.
- At [tex]\(x = 0\)[/tex], the water level [tex]\(y\)[/tex] is 40 gallons.
- At [tex]\(x = 0.5\)[/tex] minutes, the water level [tex]\(y\)[/tex] is 39.25 gallons.
- At [tex]\(x = 1\)[/tex] minute, the water level [tex]\(y\)[/tex] is 38.5 gallons.
- At [tex]\(x = 1.5\)[/tex] minutes, the water level [tex]\(y\)[/tex] is 37.75 gallons.
To determine the range of this function, we need to identify the minimum and maximum values of [tex]\(y\)[/tex] from the table.
- The minimum value of [tex]\(y\)[/tex] in the given table is 37.75 gallons.
- The maximum value of [tex]\(y\)[/tex] in the given table is 40 gallons.
The range of the function is therefore all real numbers [tex]\(y\)[/tex] such that [tex]\(37.75 \leq y \leq 40\)[/tex].
Thus, the correct answer is:
all real numbers such that [tex]\(37.75 \leq y \leq 40\)[/tex].
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.