Question

which figure correctly demonstrates using a straight line to determine that the graphed equation is not a function of x?

Explanation:

Step1: Recall the vertical line test

A relation is a function if for every \(x -\)value there is exactly one \(y -\)value. The vertical line test states that if a vertical line intersects the graph of a relation at more than one point, then the relation is not a function.

Step2: Analyze each graph

• For the first graph: A vertical line (e.g., \(x = 0\)) intersects the circle at two points.
• For the second graph: A vertical line (e.g., \(x = 4\)) intersects the circle at two points.
• For the third graph: A vertical line (e.g., \(x=2\)) intersects the circle at two points.
• For the fourth graph: A vertical line (e.g., \(x=- 2\)) intersects the circle at two points. But the question is about using a straight line (vertical line) to determine non - function. All of these graphs (circles) fail the vertical line test. However, if we consider the general concept of using the vertical line test (a straight vertical line), the third graph (the one with a vertical line drawn in the middle of the circle's right - hand side) is the one that most clearly shows the vertical line intersecting the circle (the graphed equation) at two points.

Answer:

The third graph (the one with a vertical line intersecting the circle at two points)