Question

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

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]