Question

mai wanted to study how the area of a rectangle changes with the length if its width is fixed. she computed the areas of several rectangles that have the same width and different lengths. she then plotted the results and connected them with a line, as shown below. the graph shows the area (in mm²) versus the length (in mm). find the range and the domain 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.

Explanation:

Step1: Define domain and range

Domain is the set of all possible input values (x - values, here length), range is the set of all possible output values (y - values, here area).

Step2: Determine the domain

Looking at the graph, the length (x - axis) starts from 0 and goes upwards. So the domain is \(x\geq0\).

Step3: Determine the range

The area (y - axis) starts from 0 and goes upwards. So the range is \(y\geq0\).

Answer:

Domain: \(x\geq0\), Range: \(y\geq0\)