Question

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

Answer 1

Answer:

• domain (-∞, ∞)
• range (-∞, 4]
• increasing (-∞, 0)
• decreasing (0, ∞)
• constant (only at x=0, not on any interval)

Step-by-step explanation:

The graph is of the equation y = -x^2 +4. It is a polynomial of even degree, so has a domain of all real numbers: (-∞, ∞).

The vertical extent of the graph includes y=4 and all numbers less than that:

  range: (-∞, 4]

The graph is increasing to the left of its vertex at x=0, decreasing to the right.

  increasing (-∞, 0); decreasing (0, ∞)

There is no interval on which the function is constant. It has a horizontal tangent at x=0, but a single point does not constitute an interval.