In Exercises 55–64, use the vertical line test to identify graphs in which 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, as this would imply that a single input (x-value) corresponds to multiple outputs (y-values). This test is essential for identifying functions in graphical form.

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 applying the vertical line test effectively.

Graph Interpretation

Interpreting graphs involves analyzing the visual representation of mathematical relationships. This includes understanding the axes, the shape of the graph, and how it behaves as x-values change. Effective graph interpretation is necessary to apply the vertical line test and determine whether the graph represents a function.