Question

On which interval is the function increasing? ​

Answer 1

Answer:

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

Step-by-step 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. $(-1,0)\cup (1,\infty)$