Question

A crow flies 7 miles in 11 minutes, then rests at the top of a telephone pole for 23 minutes. Write a piecewise-defined function that models the crow's journey, then sketch a graph of your function.

Answer 1

The piecewise-defined function for the crow's journey is f(t) = 7t for 0 ≤ t < 11 and f(t) = 0 for 11 ≤ t < 34. The graph is a straight line for the flying phase and a horizontal line for the resting phase.

Step-by-step explanation:

To write a piecewise-defined function that models the crow's journey, we need to consider the two different phases of the journey: the flying phase and the resting phase. Let's define the function as follows:

f(t) =

• 7t, for 0 ≤ t < 11 (flying phase)
• 0, for 11 ≤ t < 34 (resting phase)

This function represents the distance the crow travels based on the time (t) passed. In the flying phase, the crow travels at a constant speed of 7 miles per minute. During the resting phase, the crow does not move and the distance remains 0.

To sketch the graph, we plot the points (t, f(t)) for the given intervals and connect them with line segments. The graph is a straight line for the flying phase and a horizontal line for the resting phase.