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

Verified step by step guidance

1. Recall the vertical line test: A graph represents y as a function of x if and only if no vertical line intersects the graph at more than one point.
2. Examine the blue curve on the left side of the graph. Imagine drawing vertical lines at various x-values along this curve and observe if any vertical line crosses the curve more than once.
3. Do the same for the orange curve on the right side of the graph, checking if any vertical line intersects it at more than one point.
4. If for a given curve, every vertical line intersects it at most once, then y is a function of x for that curve.
5. Based on your observations, conclude which of the two curves (blue or orange) represents y as a function of x.

Key Concepts

Vertical Line Test

The vertical line test is a visual method used to determine if a graph represents a function. If any vertical line drawn through the graph intersects it at more than one point, the graph does not represent a function. This test ensures that each input (x-value) corresponds to exactly one output (y-value).

Definition of a Function

A function is a relation where each input value (x) has exactly one output value (y). This means no x-value can be paired with multiple y-values. Understanding this definition is crucial to applying the vertical line test and interpreting graphs correctly.

Graph Interpretation and Coordinate Plane

Interpreting graphs involves understanding the coordinate plane, where the horizontal axis represents x-values and the vertical axis represents y-values. Recognizing how curves behave and their position relative to the axes helps in applying tests like the vertical line test to determine function status.