Question

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.

Answer 1

Answer:

$Domain = (-\infty, \infty)$

$Range = (-\infty, 4]$

Increasing interval is: $(-\infty, 0)$

Decreasing interval is: $(0, \infty)$

Constant at no interval

Step-by-step explanation:

Given

See attachment for graph

Solving (a): The domain

From, the attached graph, we have:

$y = -x^2 + 4$

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

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

$Domain = (-\infty, \infty)$

Solving (b): The range

The curve of $y = -x^2 + 4$ opens downward, and the maximum is:

$y_{max} = 4$

This means that the minimum is:

$y_{mi n} = -\infty$

Hence, the range of the set is:

$Range = (-\infty, 4]$

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

In (a), we have:

$Domain = (-\infty, \infty)$

Split to 2 (at vertex x = 0)

$(-\infty, 0)$ and $(0, \infty)$

So:

The increasing interval is: $(-\infty, 0)$

The decreasing interval is: $(0, \infty)$

The function has a tangent at $x = 0$ but at no interval, was the function constant