Determine whether each relation defines y as a function of x. Give the domain and range. See Example 5. x-y<4

Key Concepts

Function Definition

A function is a relation where each input (x-value) corresponds to exactly one output (y-value). This means that for any given x, there cannot be two different y-values. Understanding this concept is crucial for determining if a relation qualifies as a function.

Domain and Range

The domain of a function is the set of all possible input values (x-values) that can be used without causing any mathematical inconsistencies, while the range is the set of all possible output values (y-values) that result from those inputs. Identifying the domain and range helps in understanding the behavior and limitations of the function.

Inequalities in Functions

Inequalities, such as x - y < 4, can define a region of the coordinate plane rather than a single function. Analyzing inequalities involves determining the relationship between x and y, which can help in identifying whether y can be expressed as a function of x and in finding the corresponding domain and range.