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?
Accepted Solution
A:
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]