The table below represents the displacement of a bird from its nest as a function of time:
Time
(hours)
x Displacement
from nest
(miles)
y
0 12
1 20
2 28
3 36
4 44
Part A: What is the y-intercept of the function, and what does this tell you about the bird? (4 points)
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. (4 points)
Part C: What would be the domain of the function if the bird continued to fly at this rate until it traveled 172 miles from the nest? (2 points)
Part A:
To find the y-intercept of the function represented by the table, we look at the point where x = 0. From the table, we see that when x = 0, y = 12. Therefore, the y-intercept of the function is 12.
This tells us that when the bird starts its journey (at x = 0 hours), it is already 12 miles away from its nest. So, the bird did not start its journey from the nest and was already displaced before the observation began.
Part B:
To calculate the average rate of change of the function between x = 1 and x = 3 hours, we need to determine the change in y (displacement) divided by the change in x (time).
Change in y: 36 - 20 = 16
Change in x: 3 - 1 = 2
Average rate of change = (Change in y) / (Change in x) = 16 / 2 = 8
The average rate of change of the function between x = 1 and x = 3 represents the average velocity of the bird during that time interval. In this case, it tells us that the bird covered an average of 8 miles per hour during that time range.
Part C:
The domain of a function represents the set of possible input values. In this case, x represents time in hours, and the domain would be the range of time values that make sense in the context of the problem.
Based on the given table, we can see that when x = 4 hours, the bird has traveled 44 miles from the nest. Therefore, if the bird continues to fly at the same rate, the domain of the function would be x ≤ 4, since any time greater than 4 would result in a displacement greater than 44 miles.
However, we also need to consider the condition where the bird reaches a displacement of 172 miles from the nest. From the table, we can observe that when x = 4 hours, the displacement is 44 miles. So, we need to find the additional time it would take for the bird to reach 172 miles.
Change in y = 172 - 44 = 128
Change in x = (128 / 8) = 16
Therefore, the domain of the function would be x ≤ 4 + 16 = 20, since any time beyond that would result in a displacement greater than 172 miles.
looks like you have 5 ordered pairs.
(0,12), (1,20), (2,28), (3,36) and (4,44)
it looks like for each increase of 1 in the x, the y increases by 8
so you have y = 8x + ....
and of course (0,12) is the y-intercept
y = 8x + 12
you should be able to handle the rest