Determine the largest open intervals of the domain over which each function is (c) constant. See Example 9.

Verified step by step guidance

1. Identify the sections of the graph where the function is constant.
2. Observe that the function is constant when the graph is a horizontal line.
3. Notice that the graph is a horizontal line starting from the point (0, -4) and extending to the right.
4. Determine the interval for which the function is constant. This interval starts at x = 0 and extends to positive infinity.
5. Express the interval in interval notation: [0, ∞).

Key Concepts

Domain of a Function

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. Understanding the domain is crucial for determining where a function behaves in a certain way, such as being constant. In this context, identifying the intervals where the function remains constant requires analyzing the x-values over which the function does not change.

Constant Function

A constant function is one that does not change its value regardless of the input. In graphical terms, this is represented by a horizontal line. For the given question, identifying the intervals where the function is constant involves locating sections of the graph where the y-value remains the same as x varies, which is essential for determining the largest open intervals of constancy.

Open Intervals

An open interval is a range of values that does not include its endpoints, denoted as (a, b). In the context of the question, identifying the largest open intervals where the function is constant means finding the x-values between which the function maintains a constant value without including the endpoints. This is important for accurately describing the behavior of the function over specific ranges.