Part A: The domain for Graph II is X∈ (-∞, ∞). See the definition of domain below
What is a domain?
A function's domain is the collection of all potential inputs to the function.
The domain of f(x)=x2 is all real numbers, for example, whereas the domain of g(x)=1/x is all real numbers except x=0.
Hence the other metrics are given as follows:
Part A
The range Y ∈ (-∞, ∞).
The function is increasing over X∈ (-∞, ∞). because the function on the graph has a positive slope which is constant for a straight line over the domain X∈ (-∞, ∞).
Part B
- range (-∞, 4]
- domain (-∞, ∞).
- increasing (-∞, 0)
- decreasing (0, ∞)
- constant (only at x=0, not on any interval)
Giving further 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.
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