Question

On which interval is the function increasing? ​

a (-∞-1)u(0,1)
b (-1,0)u(1,∞)
c.(-∞,-1)u(1,-∞)
d.(-1,-1)u(1,∞)

Answer 1

b.
`(-1,0)\cup (1,\infty)`

Explanation:

The graph can be divided into 4 regions.

Region 1 is for
`x\in (-\infty,-1)`

Region 2 is for
`x\in (-1,0)`

Region 3 is for
`x\in (0,1)`

Region 4 is for
`x\in (1,\infty)`

So, for the region 1, the values of
`y` goes on decreasing with increasing
`x`. Therefore, the function is decreasing in the interval
`(-\infty,-1)`.

Now, for the region 2, the values of
`y` increases with increasing
`x`. So, the function is increasing in the interval
`(-1,0)`.

For the region 3, the the values of
`y` goes on decreasing with increasing
`x`. Therefore, the function is decreasing in the interval
`(0,1)`.

Now, for the region 4, the values of
`y` increases with increasing
`x`. So, the function is increasing in the interval
`(1,\infty)`.

Therefore, regions 2 and 4 are the regions when the function is increasing.

Hence, the correct option is b.
`(-1,0)\cup (1,\infty)`