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: Identify if y is a function of x by using the vertical line test. If any vertical line intersects the graph at more than one point, then y is not a function of x.
2. Step 2: Observe the graph carefully. Notice that for each x-value, there is exactly one corresponding y-value. This means the graph passes the vertical line test, so y is a function of x.
3. Step 3: Determine the domain by looking at the x-values covered by the graph. The graph starts from approximately x = -20 and extends to the right indefinitely, so the domain is \([-20, \infty)\).
4. Step 4: Determine the range by looking at the y-values covered by the graph. The graph starts from about y = -15 and goes up to y = 30, then continues horizontally at y = 30, so the range is \([-15, 30]\).
5. Step 5: Summarize: y is a function of x, with domain \([-20, \infty)\) and range \([-15, 30]\).

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 vertical line intersects the graph at more than one point. Understanding this helps determine if y is a function of x by checking if each x has a unique y.

Domain and Range

The domain is the set of all possible x-values for which the function or relation is defined. The range is the set of all possible y-values that the function or relation can take. Identifying these sets helps describe the behavior and limits of the graph.

Vertical Line Test

The vertical line test is a visual method to determine if a graph represents a function. If any vertical line drawn through the graph intersects it more than once, the graph does not represent a function. This test is essential for analyzing the given graph.