Q:

# 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

A:
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

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PART B

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
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PART C

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