The graph below shows the distance (y) in kilometers of two cars from their destination at different times (x) in minutes. The table shows the values plotted on the graph:

Time
(in minutes)
x 0 10 20 30 40 50 60 70
Car 1
(in km)
y 70 60 50 40 30 20 10 0
Car 2
(in km)
y 70 57.19511 46.73256 38.18388 31.199 25.4919 20.82871 17.01861

Part A: What does the x-intercept of the function for car 1 represent? (2 points)

Part B: What does the y-intercept of the function for car 2 represent? (2 points)

Part C: What is the domain of the functions for car 1 and car 2? (2 points)

Part D: What is the average rate of change from x = 30 to x = 40 for the function representing the motion for car 2? What does the value of this average rate of change represent?

Part A: What does the x-intercept of the function for car 1 represent? (2 points)
For this case, the intersection with the x axis means that car 1 has reached its destination. He traveled 70 km in 70 minutes.
Part B: What does the y-intercept of the function for car 2 represent? (2 points)
For this case, the intersection with the Y axis represents that car 2 must travel 70 km to reach its destination and that it has not yet started its journey.

Part C: What is the domain of the functions for car 1 and car 2? (2 points)
car1:
The domain of the function for this car are all x that range from 0 to 70. Mathematically it can be written as [0, 70].
car 2:
The domain of the function for this car are all x that go from 0 to more infinity. Mathematically it can be written as [0, inf)

Part D: What is the average rate of change from x = 30 to x = 40 for the function representing the motion for car 2? What is the value of this average rate of change?
For the domain between x = 30 and x = 40 the rate of change of the function of the car 2 is 34.69144.
This means that car 2 travels 34.69144 km approximately in 10 minutes. As the slope is negative, then the car is getting closer to its destination.