For each graph, determine whether y is a function of x. Give the domain and range of each relation.

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 should be only one y. To determine if a relation is a function, we can use the vertical line test: if a vertical line intersects the graph at more than one point, the relation is not a function.

Domain and Range

The domain of a relation is the set of all possible input values (x-values), while the range is the set of all possible output values (y-values). For the given graph, identifying the domain and range involves observing the extent of x and y values that the graph covers. This is crucial for understanding the behavior of the function or relation represented by the graph.

Vertical Line Test

The vertical line test is a visual method used to determine if a graph represents a function. If any vertical line drawn through the graph intersects it at more than one point, the graph does not represent a function. In the case of the circle shown in the graph, vertical lines will intersect the circle at two points, indicating that y is not a function of x.