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. Step 1: Understand the definition of a function. A relation is a function if and only if each input value (x) corresponds to exactly one output value (y). This means no vertical line should intersect the graph at more than one point (Vertical Line Test).
2. Step 2: For each graph, apply the Vertical Line Test by imagining or drawing vertical lines through various x-values. If any vertical line crosses the graph more than once, then y is not a function of x for that graph.
3. Step 3: Identify the domain of the relation by determining all possible x-values for which the graph has points. The domain is the set of all these x-values.
4. Step 4: Identify the range of the relation by determining all possible y-values that the graph attains. The range is the set of all these y-values.
5. Step 5: Summarize your findings for each graph by stating whether y is a function of x, and clearly write the domain and range using interval notation or set notation as appropriate.

Key Concepts

Definition of a Function

A function is a relation where each input (x-value) corresponds to exactly one output (y-value). This means no x-value can be paired with more than one y-value. Understanding this helps determine if a graph represents a function by checking if vertical lines intersect the graph at more than one point.

Domain of a Relation

The domain is the set of all possible input values (x-values) for which the relation is defined. When analyzing a graph, the domain includes all x-values covered by the graph's points or curves. Identifying the domain helps understand the scope of the relation.

Range of a Relation

The range is the set of all possible output values (y-values) that the relation can produce. From a graph, the range includes all y-values that the graph attains. Knowing the range provides insight into the possible outputs of the relation.