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.

Explanation:

Step1: Analyze grass growth pattern

Grass height increases continuously over each week, creating an upward-sloping segment from one Wednesday to the next.

Step2: Analyze mowing effect

Every Wednesday afternoon, the grass is cut to a short, consistent height, so there is a vertical drop from the peak height (open circle, representing height before mowing) to the mowed height (closed circle, representing height after mowing) each week.

Step3: Match to correct graph

The top-left graph shows upward-sloping segments (growth) between Wednesdays, with each segment starting at a closed circle (mowed height) and ending at an open circle (pre-mow height), repeating over four weeks.

Answer:

The correct graph is the top-left option (the graph with upward-sloping segments between each Wednesday, starting at a closed circle and ending at an open circle for each weekly cycle).