The table below represents the distance of a truck from its destination as a function of time: time distance (hours) (time) x 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? (4 points) 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. (4 points) part c: what would be the domain of the function if the truck continued to travel at this rate until it reached its destination? (2 points)

Part A:
The y-intercept of the function is given when x = 0. We already have a y-value for x = 0, and that y-value is 330. 

Assuming miles is the unit used here for distance, this means that the truck was started 330 miles away from its destination.

Part B:
The average rate of change is represented by the slope of this function. We can find the slope of this function with the rise over run formula:



We are asked to use the points at x = 1 and x = 4. Plug the x and y values into the formula:

(1,275) and (4,110)


The average rate of change of the function is -55. This represents the average miles per hour the truck travels towards its destination.

Part C:
This part asks for the x-intercept of the equation. The x-intercept is defined where y = 0, which represents the destination the truck is traveling to. The domain would be restricted by the y-intercept and x-intercept, as the truck stops once it reaches its destination. We are missing the x-intercept, so we'll use the slope and the y-intercept to find it.

To find the x-intercept, we must divide the y-intercept by the slope, and subtract the result from the y-intercept's x-value:



The x-intercept is located at (6,0). The domain can be stated as follows:

2x +3y=3
7x-3y=24
solve the above equations
2x+3y=3
+7x-3y=24
9x=27
x=27/9
x=3
substitute the value of x in 2x+3y=3
2(3)+3y=3
6+3y=3
3y=3-6
3y=-3
y=-3/3
y=-1
so the solution is
{x=3,y=-1}