Question

the tabel below represents the displacement of a bird from its nest as a function of timePart A What is the y intercept of the function and what does this tell you about the bird?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 bird continued to fly at this rate until it traveled 172 miles from the nest?

Answer 1

first we will find slope

$m=\frac{20-12}{2-1}=8$

so we have equation of line is

y = mx + c

y = 8x + c

put y = 12 and x = 0

12 = 8 * 0 + c

c = 12

y = 8x + 12

y- 12 = 8x

so intercept on y is 12.

part B

the average rate of change will be

$\begin{gathered} =\frac{36-20}{3-1} \\ =\frac{16}{2} \\ =8 \end{gathered}$

so the average rate of change from x = 1 to x = 3 is 8

as the birds flies 172 miles

so put y = 172