intervals of increase and decrease are listed in terms of the ____
Intervals of increase and decrease are listed in terms of the x-values or the domain
Intervals of increase and decrease are listed in terms of the x-values or the domain.
In mathematics, an interval refers to a range of values between two points, and it can be applied to the x-axis or the domain when analyzing the behavior of a function. When we talk about intervals of increase and decrease, we are referring to the intervals on the x-axis where the function is either increasing or decreasing.
To determine the intervals of increase and decrease, we need to examine the slope of the function. A positive slope indicates an increasing function, while a negative slope indicates a decreasing function. When the slope of the function changes from positive to negative or vice versa, it indicates a turning point or a local extremum.
Therefore, to find the intervals of increase and decrease, we look for the x-values or the domains where the function’s slope changes sign. These x-values act as the boundaries for the intervals. For example, if we have a function f(x) and it changes from increasing to decreasing at x = a, and then changes back to increasing at x = b, the intervals of increase and decrease would be (−∞, a) and (a, b), respectively.
By listing the intervals in terms of the x-values or the domain, we can easily understand the behavior of the function and identify where it is increasing or decreasing on the x-axis.
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