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 is a method to determine if a graph represents a function. If any vertical line drawn on the graph intersects the curve at more than one point, then the graph does not represent a function.
2. Step 2: Observe the graph provided. The graph shows a red curve plotted on a Cartesian plane. The x-axis and y-axis are labeled, and the curve appears to be continuous.
3. Step 3: Apply the vertical line test. Imagine drawing vertical lines at various x-values across the graph. Check if any vertical line intersects the red curve at more than one point.
4. Step 4: Analyze the intersections. For this graph, every vertical line intersects the red curve at exactly one point, regardless of the x-value chosen.
5. Step 5: Conclude based on the test. Since no vertical line intersects the curve at more than one point, the graph passes the vertical line test. Therefore, y is a function of x for this graph.

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 of x. This test is crucial for identifying whether y is a function of x, as it ensures that each input (x-value) corresponds to exactly one output (y-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. In mathematical terms, for a relation to be a function, it must satisfy the condition that no two ordered pairs have the same first element with different second elements. Understanding this definition is essential for applying the vertical line test effectively.

Graph Interpretation

Graph interpretation involves analyzing the visual representation of mathematical functions on a coordinate plane. It requires understanding how the shape and behavior of a graph relate to the properties of the function it represents. This skill is vital for applying the vertical line test and determining the nature of the relationship between x and y in the given graph.