The table below represents the distance of a car from its destination as a function of time: Time (hours) x Distance (miles) y 0 900 1 850 2 800 3 750 Part A: What is the y-intercept of the function, and what does this tell you about the car? (4 points) Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 3, and tell what the average rate represents. (4 points) Part C: What would be the domain of this function if the car traveled the same rate until it reached its destination? (2 points)

Accepted Solution

x (Time in Hours)         y (Distance)
   0                                    900
   1                                     850
   2                                    800
   3                                    750

The y-intercept of this function would be the value of y when x = 0
Reading from the table, when x = 0, y = 900
Interpreting this value it means that initially, the distance of the car from its destination is 900 miles


The rate of change is calculated by finding the vertical and horizontal distance between two points

The decrease is the same value every time; for every hour, there's a decrease of 50 miles.

So, the rate of change is 50 miles per hour


The function is in the straight line equation form: y = -50x + 900
The value -50 represents the negative slope (the decrease in distance)
The value 900 represents the y-intercept
The car reaches its destination when y = 0, so the value of x would be

0 = -50x + 900
50x = 900
x = 900/50
x = 18 hours

The domain of the function is 0 ≤ x ≤ 18