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
------------------------------------------------------------------------------------------------------------ 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 ------------------------------------------------------------------------------------------------------------
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