Determine the intervals of the domain for which each function is (a) increasing, (b) decreasing,

step 1 This question shows us the graph of a function and it asks us where is it increasing and where i

Determine the intervals of the domain for which each...

Key Concepts

Interval/Domains Analysis

Intervals in the context of function analysis refer to continuous subsets of the domain over which the behavior of the function (increasing, decreasing, or constant) is consistent. Determining such intervals involves analyzing the function's graph or its derivative (when applicable) to identify where these properties hold across the domain.

Constant Function

A constant function maintains the same output value for every input within a certain interval. This means that for any two numbers x1 and x2 in that interval, f(x1) = f(x2). Constant behavior is a special case of monotonicity where there is no change in the function value regardless of changes in the input.

Decreasing Function

A decreasing function is one in which the function values fall as the input values increase. In other words, for any two points x1 and x2 in the domain with x1 < x2, the inequality f(x1) > f(x2) is satisfied. This property is important for analyzing how a function's output changes relative to its input, indicating a downward trend over intervals.

Increasing Function

An increasing function is one in which the function values rise as the input values increase. This means that for any two numbers x1 and x2 in the domain with x1 < x2, the inequality f(x1) < f(x2) holds. This concept is fundamental to understanding the behavior of functions as it relates to their monotonic nature.

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