Question

What is the rate of change of the function represented by the table?

x
y
1
5
2
5
3
5
4
5
0
1
4
5

Answer 1

I’m not sure I’m reading the table correctly — it looks ambiguous. Two reasonable readings and their answers:

1) If the table is
x: 1, 2, 3, 4
y: 5, 5, 5, 5
then y is constant, so the rate of change = 0.

2) If the table is just the two points (0,1) and (4,5),
then the average rate of change (slope) = (5 − 1)/(4 − 0) = 1.

If the table actually contains all points (0,1), (1,5), (2,5), (3,5), (4,5), there is no single constant rate of change; you can compute an average rate between any two x-values (for example from 0 to 4 it is (5−1)/(4−0)=1, but from 0 to 1 it is (5−1)/(1−0)=4, and between consecutive x from 1 to 2 it is 0).

Which interpretation did you mean?