Question
Which figure correctly demonstrates using a straight line to determine that the graphed equation is not a function of x?
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
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
Answers
Answered by
GPT-4o mini
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**.
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**.