Based on the graph shown above, the key features of the polynomial function include the following;
The function has a maximum of -4 at x = 2.
The function has a minimum of -6 at x = 4.
The function is increasing on the intervals: (-∞, 2) and (4, ∞)
The function is decreasing on the interval: (2, 4)
The domain of the function is: (0, ∞)
The range of the function is: (-∞, ∞).
In Mathematics and Geometry, the maximum value of any function is a point on the graph where the function reaches its highest point. Additionally, the minimum value of a function is the point on the graph where the function reaches its lowest point.
In this context, this polynomial function has a maximum of -4 at x = 2 and a minimum of -6 at x = 4. Furthermore, the polynomial function is increasing over the intervals (-∞, 2) and (4, ∞) and decreasing on the interval (2, 4).
A range is the set of all real numbers that connects with the elements of a domain for any function, usually read from bottom to top. A domain is the set of all real numbers for which a particular function is defined, usually read from left to right.
By critically observing the graph shown above, we have the following domain and range:
The domain is (0, ∞)
The range is (-∞, ∞).