Questions: During the first two weeks in May, a man weighs himself daily (in pounds) and records the data in the table below. Full data set प्र 1 2 3 4 5 6 7 Weight (lbs) 199 200 199 200 199 198 197 May 8 9 10 11 12 13 14 Weight (lbs) 196 197 196 195 194 195 194 a. Does the table define weight as a function of the day in May? No Yes b. What is the domain of this function? A. 194,195,196,197,198,199,200 pounds B. 1,2,3,4,5,6,7,8,9,10,11,12,13,14 day C. All the days in May D. All real numbers c. What is the range? A. 194,195,196,197,198,199,200 pounds B. 1,2,3,4,5,6,7,8,9,10,11,12,13,14 day C. All the days in May D. All real numbers d. During what day(s) did he weigh the most? Day(s): (Use a comma to separate answers as needed.) e. During what day(s) did he weigh the least? Day(s): (Use a comma to separate answers as needed.) f. He claimed to be on a diet. What is the longest period of time during which his weight decreased? The longest period of time where his weight decreased was days.

During the first two weeks in May, a man weighs himself daily (in pounds) and records the data in the table below. Full data set प्र 1 2 3 4 5 6 7 Weight (lbs) 199 200 199 200 199 198 197 May 8 9 10 11 12 13 14 Weight (lbs) 196 197 196 195 194 195 194 a. Does the table define weight as a function of the day in May? No Yes b. What is the domain of this function? A. 194,195,196,197,198,199,200 pounds B. 1,2,3,4,5,6,7,8,9,10,11,12,13,14 day C. All the days in May D. All real numbers c. What is the range? A. 194,195,196,197,198,199,200 pounds B. 1,2,3,4,5,6,7,8,9,10,11,12,13,14 day C. All the days in May D. All real numbers d. During what day(s) did he weigh the most? Day(s): (Use a comma to separate answers as needed.) e. During what day(s) did he weigh the least? Day(s): (Use a comma to separate answers as needed.) f. He claimed to be on a diet. What is the longest period of time during which his weight decreased? The longest period of time where his weight decreased was days.
Transcript text: During the first two weeks in May, a man weighs himself daily (in pounds) and records the data in the table below. \begin{tabular}{|l|c|c|c|c|c|c|c|} \hline \multicolumn{9}{|c|}{ Full data set प्र } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline Weight (lbs) & 199 & 200 & 199 & 200 & 199 & 198 & 197 \\ \hline May & 8 & 9 & 10 & 11 & 12 & 13 & 14 \\ \hline Weight (lbs) & 196 & 197 & 196 & 195 & 194 & 195 & 194 \\ \hline \end{tabular} a. Does the table define weight as a function of the day in May? No Yes b. What is the domain of this function? A. $\{194,195,196,197,198,199,200\}$ pounds B. $\{1,2,3,4,5,6,7,8,9,10,11,12,13,14\}$ day C. All the days in May D. All real numbers c. What is the range? A. $\{194,195,196,197,198,199,200\}$ pounds B. $\{1,2,3,4,5,6,7,8,9,10,11,12,13,14\}$ day C. All the days in May D. All real numbers d. During what day(s) did he weigh the most? Day(s): $\square$ (Use a comma to separate answers as needed.) e. During what day(s) did he weigh the least? Day(s): $\square$ (Use a comma to separate answers as needed.) f. He claimed to be on a diet. What is the longest period of time during which his weight decreased? The longest period of time where his weight decreased was $\square$ days.
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Solution

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Solution Steps

Step 1: Determine if weight is a function of the day

A function is defined as a relation where each input (day) corresponds to exactly one output (weight). In the table, each day has exactly one weight value associated with it. Therefore, weight is a function of the day.

Conclusion: Yes, the table defines weight as a function of the day.

Step 2: Identify the domain of the function

The domain of a function is the set of all possible input values (days). From the table, the days are \(1, 2, 3, \dots, 14\).

Conclusion: The domain is \(\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14\}\) days.

Step 3: Identify the range of the function

The range of a function is the set of all possible output values (weights). From the table, the weights are \(194, 195, 196, 197, 198, 199, 200\) pounds.

Conclusion: The range is \(\{194, 195, 196, 197, 198, 199, 200\}\) pounds.

Final Answer

a. Does the table define weight as a function of the day in May?
\(\boxed{\text{Yes}}\)

b. What is the domain of this function?
\(\boxed{\text{B. }\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14\} \text{ day}}\)

c. What is the range?
\(\boxed{\text{A. }\{194, 195, 196, 197, 198, 199, 200\} \text{ pounds}}\)

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