Question

The average rate of change of a function is less from = x equals 1 to = x equals 4 than from = x equals 5 to = x equals 8 . What type of function could it be? Explain

Answer 1

Explanation:

Given that,

Rate of change of a function

1. From x = 1 to x = 4

2. From x = 5 to x =8

Then,

Rate of change for first condition

∆x/∆t = (x2-x1) / (t2-t1)

∆x/∆t = (4-1) / (t2-t1)

∆x/∆t = 3 / (t2-t1)

Rate of change for second condition

∆x/∆t = (x2-x1) / (t2-t1)

∆x/∆t = (8-5) / (t2-t1)

∆x/∆t = 3 / (t2-t1)

The rate of change are equal, it shows that the slope are equal.

So, it is a straight line function.

Since it has equal rate of change..