Question

The table below represents the displacement of a bird from its nest as a function of time:

Answer 1

The y-intercept (point where x, or time equals zero), is 12 miles. This means that when observation of the bird began at time t=0, it was already away from its nest. Based on the rest the graph, one can infer that the bird has a very large range (travels far from her nest) and spends a great deal of time away from her nest. 

To find the average rate of change of the function, take the change in y between x=1 and x=3 and divide by 2. 
(36 - 20) / 2 = 16/2 = 8 miles / hour .

The domain of the function is the range of x for which y is a real number. We see in the chart provided that the bird travels 8 miles every hour. 

How many hours will it take to travel 172 miles from the nest? The bird started at 12, so let's so how long it takes to travel 172 - 12 = 160 miles, moving at a rate of 8 miles/hour.
160 miles / 8mph = 20 hours
The domain of the function, the time range in which the bird travels 172 miles from the nest, will be 0 ≤ x ≤ 20