Question

Determine the average rate of change for each interval in the graph
interval | average rate of change
r = -2 to r = 1 | ?
r = -2 to r = 5 | ?
r = -2 to r = 8 | ?

the graph has points at 6, 5, 8, and 15

Answer 1

I'll assume the function values at the listed r-values are:
f(-2)=6, f(1)=5, f(5)=8, f(8)=15.

Average rate of change on [a,b] = (f(b) − f(a)) / (b − a).

- r = −2 to r = 1: (5 − 6) / (1 − (−2)) = −1 / 3 ≈ −0.333...
- r = −2 to r = 5: (8 − 6) / (5 − (−2)) = 2 / 7 ≈ 0.2857
- r = −2 to r = 8: (15 − 6) / (8 − (−2)) = 9 / 10 = 0.9

Let me know if the point-ordering is different and I can recompute.