Question

does the relation shown below define a function? yes no

Explanation:

Step1: Recall the definition of a function

A relation is a function if every input (x - value) has exactly one output (y - value). One way to test this is the vertical line test: if any vertical line drawn through the graph intersects the graph at more than one point, then the relation is not a function.

Step2: Analyze the given graph

The given graph is an ellipse (or a closed curve). If we draw a vertical line through the graph, for some x - values (within the domain of the ellipse), the vertical line will intersect the graph at two points (one above and one below the x - axis or on either side of the vertical line of symmetry). For example, consider the vertical line that passes through the center of the ellipse (assuming the center is at some point on the x - axis or y - axis). This vertical line will intersect the ellipse at two different y - values. So, the graph fails the vertical line test.

Answer:

No (the option "No" should be selected as the graph does not represent a function because it fails the vertical line test, meaning there are x - values with more than one corresponding y - value)