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

Question

On a coordinate plane, a circle is centered around (0, 0). A vertical line touches the edge of the circle at (negative 4, 0).
On a coordinate plane, a circle is centered around (0, 0). A horizontal line touches the edge of the circle at (0, 4).
On a coordinate plane, a circle is centered around (0, 0). A vertical line goes through 2 points of the circle
On a coordinate plane, a circle is centered around (0, 0). A horizontal line goes through 2 points of the circle

Answer 1

To determine whether a graphed equation is a function of \( x \), you can use the Vertical Line Test. According to this test, if a vertical line can intersect the graph at more than one point, then the graph does not represent a function of \( x \).

In the context of your options:

1. A vertical line touches the edge of the circle at (negative 4, 0) — This line only touches one point, which indicates it could be a function.
2. A horizontal line touches the edge of the circle at (0, 4) — This line also only touches one point, which does not help to determine if it's a function of \( x \).
3. A vertical line goes through 2 points of the circle — This indicates that the vertical line intersects the circle at two points. Therefore, this shows that the relation is not a function of \( x \).
4. A horizontal line goes through 2 points of the circle — This indicates that although a horizontal line intersects the circle at two points, it is not directly relevant for determining if it's a function of \( x \).

Thus, the correct figure that demonstrates using a straight line to determine that the graphed equation is not a function of \( x \) is the vertical line that goes through 2 points of the circle.