Question

A homeowner mows the lawn every Wednesday afternoon. Sketch a rough graph of the height of the grass as a function of time over the course of a four-week period.

Short answer

The required graph is as follows.

Step-by-step solution

Describe the given information

It is required to sketch the graph of the height of the grass versus time over the course of a four-week period

Sketch a graph of the height of the grass as a function of time over the course of a four-week period

Consider that every Wednesday afternoon a homeowner cuts the grass. So, the initial height of the grass would be low on the first week of Wednesday.

During the period from Wednesday to Wednesday, the height of the grass will increase gradually, and then on the second week of Wednesday, again the grass gets cut.

So, the height of the grass would instantly become shorter. This change can be shown on the graph as a gap between a higher \(y\) value and a lower \(y\) value. This same pattern would repeat three more times.

Each week, the grass would gradually increase in height, and then instantly become shorter each Wednesday.

Draw the required graph as follows.