Question

1. a city maintenance worker is filling up a 15,000 gallon community swimming pool. the graph shows the remaining volume to fill the pool as a linear function of x, the time in hours. which answer choice best describes the domain and range of the function for this situation? filling a swimming pool graph of a line from (0,15) to (25,0) with x-axis labeled time (hours) and y-axis labeled volume remaining (thousands of gallons) a. domain: all real numbers greater than or equal to 0 and less than or equal to 25; range: all real numbers greater than or equal to 0 and less than or equal to 15 b. domain {25}; range {15} c. domain: all real numbers greater than or equal to 0 and less than or equal to 15; range: all real numbers greater than or equal to 0 and less than or equal to 25 d. domain {15}; range {25}

Explanation:

Step1: Understand Domain and Range

Domain is the set of x - values (time in hours) for the function. From the graph, the time starts at \(x = 0\) (when filling starts) and ends at \(x=25\) (when the pool is full, since the remaining volume is 0 at \(x = 25\)). So the domain is all real numbers from 0 to 25, inclusive.

Range is the set of y - values (remaining volume in thousands of gallons). The remaining volume starts at \(y = 15\) (when \(x = 0\), the pool is empty and needs 15,000 gallons) and goes down to \(y = 0\) (when \(x=25\), the pool is full). So the range is all real numbers from 0 to 15, inclusive.

Step2: Analyze the Options

• Option A: Domain: \(0\leq x\leq25\), Range: \(0\leq y\leq15\) which matches our analysis.
• Option B: Domain and Range as single values is incorrect as time and volume change over an interval.
• Option C: Swapped domain and range, which is incorrect.
• Option D: Domain and Range as single values is incorrect.

Answer:

A. Domain: All real numbers greater than or equal to 0 and less than or equal to 25; Range: All real numbers greater than or equal to 0 and less than or equal to 15