The table below represents the velocity of a car as a function of time:
Time
(hour)
x Velocity
(miles/hours)
y
0 50
1 52
2 54
3 56
Part A: What is the y-intercept of the function, and what does this tell you about the car?
Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 3 hours, and tell what the average rate represents.
Part C: What would be the domain of the function if the velocity of the car was measured until it reached 60 miles/hour and the car does not change motion?
y-intercept is where x=0.
avg rate is (56-52)/(3-1)
Looks like that would be 2 more hours. So, {0..5}
Thank You
Part A: To find the y-intercept of the function, you need to identify the value of y when x = 0. Looking at the table, when x = 0, y = 50. The y-intercept of the function is 50.
The y-intercept represents the starting point of the car's velocity when time (x) is zero. In this case, the car's velocity is 50 miles per hour at the beginning.
Part B: To calculate the average rate of change between x = 1 and x = 3 hours, you need to find the difference in y values (velocity) divided by the difference in x values (time).
Average rate of change = (change in y) / (change in x)
= (54 - 52) / (2 - 1)
= 2 / 1
= 2
The average rate of change of the function between x = 1 to x = 3 hours is 2. In this context, it represents the average increase in velocity (in miles per hour) per hour during that time interval.
Part C: The domain of a function represents the set of all possible input values. In this case, if the velocity of the car reaches 60 miles/hour and the car does not change its motion, the domain of the function would be limited to the time it takes for the car to reach that velocity.
Given the table, we can observe that the velocity increases by 2 miles per hour every hour. So, if the car initially starts at 50 miles/hour and increases by 2 miles/hour, it would take approximately 5 hours to reach 60 miles/hour (50 + 2 * 5 = 60).
Therefore, the domain of the function would be x values from 0 to 5 hours, including both endpoints: [0, 5].