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

step 1 This question gives us a graph of a function and asks us where it's increasing and decreasing. I

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

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Key Concepts

Constant Function

A function is constant on an interval when the output remains the same for every input within that interval. In such cases, f(x) does not change regardless of changes in x. This concept helps distinguish parts of a function’s graph where no vertical movement occurs, compared to areas where the function is either increasing or decreasing.

Decreasing Function

A function is decreasing on an interval if, for any two points within the interval, the function yields a smaller value when the input is larger. That means as x increases, f(x) decreases. Recognizing decreasing intervals is important in studying the behavior and trends of functions.

Domain of a Function

The domain of a function is the complete set of all possible values of the independent variable (often x) for which the function is defined. Understanding the domain is crucial as it establishes the intervals over which the function's behavior—whether increasing, decreasing, or constant—is analyzed.

Increasing Function

A function is said to be increasing on an interval if, whenever one point is to the right of another, the function's value at that point is higher. In other words, as x increases, f(x) also increases. This concept is essential in calculus and graph analysis to understand how the output of a function changes with respect to its input.

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