Question

e owners of a recreation area filled a small pond with water in 100 minutes. the pond already had some water at the beginning. the graph shows the amount of water (in liters) in the pond versus time (in minutes). find the domain and the range of the function shown. write your answers as inequalities, using x or y as appropriate. or, you may instead click on \empty set\ or \all reals\ as the answer. domain: range:

Explanation:

Step1: Determine the domain

The x - axis represents time (in minutes). From the graph, the left - most point has \(x = 0\) and the right - most point has \(x=100\). So the domain is the set of all \(x\) values such that \(0\leq x\leq100\).

Step2: Determine the range

The y - axis represents the amount of water (in liters). The lowest value of \(y\) (at \(x = 100\)) is \(1200\) liters and the highest value of \(y\) (at \(x = 0\)) is \(450\) liters? Wait, no, looking at the graph, the starting point (when \(x = 0\)) has \(y=450\) and the ending point (when \(x = 100\)) has \(y = 1200\)? Wait, no, the coordinates: the first point is \((0,450)\) and the second point is \((100,1200)\)? Wait, no, the y - axis is labeled with 0, 150, 300, 450, 600, 750, 900, 1050, 1200, 1350, 1500. The blue line starts at \((0,450)\) and ends at \((100,1200)\)? Wait, no, the x - axis is time (minutes) from 0 to 180, and the y - axis is amount of water (liters). Wait, the two points: one at \(x = 0\), \(y=450\) and one at \(x = 100\), \(y = 1200\)? Wait, no, the graph: the left point is at \(x = 0\), \(y = 450\) (since 450 is on the y - axis) and the right point is at \(x=100\), \(y = 1200\) (since 1200 is on the y - axis). So the range is the set of all \(y\) values such that \(450\leq y\leq1200\). Wait, no, maybe I got the direction wrong. Wait, if the pond is being filled, the amount of water should increase over time. So at \(x = 0\) (time = 0), the amount of water is 450 liters, and at \(x = 100\) (time = 100 minutes), the amount of water is 1200 liters. So the domain (x - values) is from 0 to 100, so \(0\leq x\leq100\). The range (y - values) is from 450 to 1200, so \(450\leq y\leq1200\).

Answer:

Domain: \(0\leq x\leq100\)
Range: \(450\leq y\leq1200\)