Question

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?

Answer 1

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.