State the domain, the range, and the intervals on which function is increasing decreasing, or constant in interval notation. State the domain and range using interval notation.

Increasing interval is:

Decreasing interval is:

Constant at no interval

Step-by-step explanation:

Given

See attachment for graph

Solving (a): The domain

From, the attached graph, we have:

The degree of the polynomial (i.e 2) is even.

Hence, the domain is the set of all real numbers, i.e.

Solving (b): The range

The curve of opens downward, and the maximum is:

This means that the minimum is:

Hence, the range of the set is:

Solving (c): Interval where the function increases/decreases/constant

In (a), we have:

Split to 2 (at vertex x = 0)

and

So:

The increasing interval is:

The decreasing interval is:

The function has a tangent at but at no interval, was the function constant