Question

Use interval notation to write the intervals over which is (a) increasing, (b) decreasing, and (c) constant.please check photo

Answer 1

Given:

The graph of the function is given.

Required:

We have to find the intervals over which f is

(a) Increasing.

(b) Decreasing.

(c) Constant.

Step-by-step explanation:

If the graph of the function goes up in any interval then we say that the function is increasing over that interval.

If the graph of the function goes down in any interval then we say that the function is decreasing over that interval.

If the graph of the function is parallel to the x-axis in any interval then we say that the function is constant over that interval.

In the figure, we can see that the graph of the function goes up in the interval (0.-1) and the graph of the function goes down in any interval (2,3). And it is parallel to the x-axis in the interval (1.2).

Final answer:

Hence the final answer is

(a) The function is increasing in the interval

`(0,-1).`

The function is decreasing in the interval

`(2,3).`

The function is constant in the interval

`(0,2).`

Part 1 of 3:

The function is sometimes increasing

`\text{ Increasing interval}=(0,-1).`

Part 2 of 3:

The function is sometimes decreasing