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?

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.

part c: what would be the domain of the function if the airplane continued to travel at this rate until it reached its destination?

Let us first find the equation for the distance as a function of time in the form:

d=mx+b

m=(d2-d1)/(x2-x1)

m=(2160-2700)/(1-0)

m=-540

d=-540x+b, using point (0,2700) we can solve for b

2700=-540(0)+b

2700=b so

d(x)=-540x+2700

A)  The y-intercept is the constant of our distance function  (the distance when x, time, equals zero).  In this case d=2700 is the y-intercept.  This means that the initial distance from the destination was 2700 miles.

B) Since this is just a line and has a constant velocity, its average velocity will just be the constant velocity or slope.  But mathematically we could show this to be true.  Average velocity is change in distance divided by change in time.

v=(540-2160)/(4-1)

v=-1620/3

v=-540 mph

C)

The domain of a function is the possible x values in the proper context.  First time cannot be less than 0.  The other extreme for time is when the plane reaches its destination, when d=0, which is when:

-540x+2700=0

540x=2700

x=5.  

So the plane reaches its destination after 5 hours.  So the domain, the x values, for d=-540x+2700 is

x=[0,5]