Given: Graph of the function.
Required: Open interval of the domain for which the function is
(a) increasing
(b) decreasing
(c) constant
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
[tex](2,\infty)[/tex]
(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
[tex](-\infty,-2)[/tex]
(c) constant
The function remains constant in the open interval
[tex](-2,2)[/tex]
Final answer:
The function is
(a) increasing in
[tex](2,\infty)[/tex]
(b) decreasing in
[tex](-\infty,-2)[/tex]
(c) constant in
[tex](-2,2)[/tex]
