Question

Determin the open intervals of the domain for the the function shown in the graph below

Answer 1

Given: Graph of the function.

Required: Open interval of the domain for which the function is

(a) increasing

(b) decreasing

(c) constant

Step-by-step explanation:

Firstly, if we see from left hand side, function is coming downwards that is it is decreasing.

Then at a point, it stops decreasing and become constant.

Then after a point it starts going upwards, that it starts to increase.

Now,

(a) increasing

The function starts increasing at x = 2, and it keeps on increasing after that (as the arrow suggests)

So the open interval in which the function is increasing is

`(2,\infty)`

(b) decreasing

The function is decreasing in the beginning, and it decreases till x = -2

So the open interval in which the function is decreasing is

`(-\infty,-2)`

(c) constant

The function remains constant in the open interval

`(-2,2)`

Final answer:

The function is

(a) increasing in

`(2,\infty)`

(b) decreasing in

`(-\infty,-2)`

(c) constant in

`(-2,2)`