Question

determine whether the following graph represents a function.

the graph represent
a function because
is mapped
to .

Explanation:

Step1: Recall the vertical line test

A graph represents a function if every vertical line intersects the graph at most once. For a relation to be a function, each input (x - value) must have exactly one output (y - value).

Step2: Apply the vertical line test to the given graph

The given graph is an ellipse (a closed curve). If we draw a vertical line (for example, the line \(x = 1\) or \(x = 0\) or any vertical line that passes through the ellipse), it will intersect the ellipse at more than one point. This means that there are x - values that are mapped to more than one y - value. For instance, consider the x - value in the domain of the ellipse, it will correspond to two different y - values (one from the upper part of the ellipse and one from the lower part). So, the graph does not pass the vertical line test.

Answer:

The graph does not represent a function because at least one x - value is mapped to more than one y - value.