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?

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]