Question

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

Time (hours) x Distance (miles) y
          0                   330
          1                    275
          2                   220
         3                    165
         4                    110
Part A: What is the y-intercept of the function, and what does this tell you about the truck?
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 truck continued to travel at this rate until it reached its destination?

Answer 1

Part A: What is the y-intercept of the function, and what does this tell you about the truck?
The intersection of a function with the y-axis occurs when we evaluate the function for x = 0.
For this case we have:
f (0) = 330 miles
Therefore, the intersection with the y-axis is 330 miles.
It means that the truck is 330 miles from its destination.

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.
Since the function is linear, the average exchange rate is:
m = (y2-y1) / (x2-x1)
Substituting values:
m = (275-330) / (1-0)
m = -55
It represents that the truck approaches 55 miles every hour to its destination.

Part C: What would be the domain of the function if the truck continued to travel at this rate until it reached its destination?
The linear equation that represents the problem is:
y = -55x + 330
For y = 0 we have:
0 = -55x + 330
Clearing x:
x = 330/55
x = 6
The domain of the function will be:
[0, 6]