Use the vertical line test to identify graphs in which y is a function of x.

Verified step by step guidance

1. Step 1: Understand the vertical line test. The vertical line test states that a graph represents a function if and only if no vertical line intersects the graph at more than one point.
2. Step 2: Visualize or draw vertical lines across the graph. Imagine or draw several vertical lines (parallel to the y-axis) across different parts of the graph.
3. Step 3: Check intersections. Observe each vertical line and count the number of points where it intersects the graph.
4. Step 4: Analyze the intersections. If any vertical line intersects the graph at more than one point, then y is not a function of x. If every vertical line intersects the graph at most once, then y is a function of x.
5. Step 5: Conclude based on the analysis. Based on the intersections observed, determine whether the graph passes the vertical line test and thus whether y is a function of x.

Key Concepts

Vertical Line Test

The vertical line test is a method used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph does not represent a function. This is because a function must assign exactly one output (y-value) for each input (x-value).

Function Definition

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output. This means that for every x-value in the domain, there is a unique y-value in the range. Understanding this definition is crucial for identifying functions from graphs.

Graph Interpretation

Graph interpretation involves analyzing the visual representation of data or functions on a coordinate plane. It requires understanding the axes, the scale, and the shape of the graph to draw conclusions about the relationship between variables. This skill is essential for applying the vertical line test effectively.