Find the interval(s) over which the function is increasing

Answer : (-∞,-1) U  (-1, 1)

We need to find  the interval(s) over which the function is increasing

We look at the intervals of x  where the graph is increasing

Increasing interval of the graph is the part where the graph goes up.

At first  the graph starts increasing and it increases till x=-1

So the first increasing interval is -infinity to -1 . We write it as (-∞,1)

Now, we look at the part where the graph changes direction

In the middle  inverted U shaped graph , the graph starts increasing at x=-1  and increases till it changes direction. The graph is increasing till x=1

so second increasing interval is x=-1  to 1. we write it as (-1,1)

Now combine both intervals by a 'U' union

(-∞,-1) U  (-1, 1)

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according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

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