The table below represents the distance of an airplane from its destination as a function of time:

Time
(hours)
x Distance
(miles)
y
0 2,700
1 2,160
2 1,620
3 1,080
4 540

Part A: What is the y-intercept of the function, and what does this tell you about the airplane? (4 points)

Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 4 hours, and tell what the average rate represents. (4 points)

Part C: What would be the domain of the function if the airplane continued to travel at this rate until it reached its destination? (2 points)

Part A:

To find the y-intercept of the function represented by the table, we need to consider the point where the x-coordinate is 0. Looking at the table, we see that when x = 0, the distance (y) is 2,700 miles. Therefore, the y-intercept of the function is 2,700.

The y-intercept represents the initial distance of the airplane from its destination when the time is zero. In this case, it tells us that the airplane was initially 2,700 miles away from its destination.

Part B:

To calculate the average rate of change of the function represented by the table between x = 1 to x = 4 hours, we need to find the change in distance (y) divided by the change in time (x).

Change in distance = Final distance - Initial distance
= Distance at x = 4 - Distance at x = 1
= 540 - 2,160
= -1,620

Change in time = Final time - Initial time
= 4 - 1
= 3

Average rate of change = Change in distance / Change in time
= -1,620 / 3
= -540 miles per hour

The average rate of change of -540 miles per hour represents the average speed at which the distance from the destination is decreasing between x = 1 to x = 4 hours. It indicates that the airplane is getting closer to its destination at a rate of 540 miles per hour during this time period.

Part C:

The domain of the function represents all possible values of x. In this case, since the airplane continued to travel at the same rate until it reached its destination, the domain would be the set of all real numbers greater than or equal to 0. This means the airplane can continuously travel for any non-negative amount of time until it reaches its destination.

What is your question about how to do this?