Ask AI: Suppose f is a function defined on an interval I. Define the following, (1) increasing (2) decreasing (3) constant

Sure, I can help define these terms as they are used in mathematical functions. (1) Increasing: A function f is considered increasing on an interval I if for any two numbers x1 and x2 in I, if x1 < x2, then f(x1) <= f(x2). This means that as you move from left to right on the graph of the function, the y-values (or outputs of the function) are getting larger or staying the same. (2) Decreasing: A function f is said to be decreasing on an interval I if for any two numbers x1 and x2 in I, if x1 < x2, then f(x1) >= f(x2). This means that as you move from left to right on the graph of the function, the y-values (or outputs of the function) are getting smaller or staying the same. (3) Constant: A function f is constant on an interval I if for any two numbers x1 and x2 in I, f(x1) = f(x2). This means no matter what x-value you plug into the function within that interval, the output will always be the same. On a graph, a constant function appears as a horizontal line.