Question

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

Answer 1

Answer : (0,3) U  (3, ∞)

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

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

Decreasing interval of the graph is the part where the graph goes down

We look at the part where the graph changes direction

In the middle  inverted U shaped graph , the graph changes direction and start decreasing at x=0

the graph is decreasing till x=3

so first decreasing interval is x=0  to 3. we write it as (0,3)

After x=3 the graph starts decreasing and it goes to infinity

So the second decreasing interval is 3  to infinity . We write it as (3, ∞)

Now combine both intervals by a 'U' union

(0,3) U  (3, ∞)