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

Verified step by step guidance

1. Examine the graph to determine if y is a function of x by checking if any vertical line intersects the graph at more than one point.
2. Notice that at x = 0, there are two different y-values (y = 2 and y = 4), which means y is not a function of x.
3. Identify the domain of the relation by observing the x-values covered by the graph. The domain is all real numbers.
4. Identify the range of the relation by observing the y-values covered by the graph. The range is y ≤ 2 or y ≥ 4.
5. Conclude that y is not a function of x because it fails the vertical line test, and provide the domain and range as described.

Key Concepts

Function Definition

A function is a relation where each input (x-value) corresponds to exactly one output (y-value). To determine if y is a function of x, we can use the vertical line test: if a vertical line intersects the graph at more than one point, then y is not a function of x.

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 issues, such as division by zero. The range is the set of all possible output values (y-values) that result from the domain. Identifying the domain and range involves analyzing the graph to see the extent of x and y values.

Graph Interpretation

Interpreting graphs involves understanding the visual representation of mathematical relationships. This includes recognizing shapes, trends, and points of intersection. In this case, analyzing the curves and their intersections helps determine if y is a function of x and aids in identifying the domain and range.