To determine which graph shows a set of ordered pairs that represents a function, we need to use the vertical line test. A graph represents a function if and only if a vertical line drawn at any x-coordinate intersects the graph at exactly one point.
Let's examine each option:
1. On a coordinate plane, solid circles appear at the following points: (-5, 4), (-3, 2), (-1, 3), (1, 1), (1, -2), (3, -3).
- Here, the x-coordinate 1 is paired with both 1 and -2. Thus, a vertical line at x = 1 intersects the graph at two points. This set is **not** a function.
2. On a coordinate plane, solid circles appear at the following points: (-5, 2), (-4, -4), (-3, 4), (-2, 2), (2, -2), (4, 3).
- Here, each x-coordinate has a unique y-coordinate. Thus, any vertical line intersects the graph at most once. This set **is** a function.
3. On a coordinate plane, solid circles appear at the following points: (-4, 2), (-1, 4), (1, 0), (2, 3), (2, -3), (3, 1).
- Here, the x-coordinate 2 is paired with both 3 and -3. Thus, a vertical line at x = 2 intersects the graph at two points. This set is **not** a function.
4. On a coordinate plane, solid circles appear at the following points: (-4, 2), (-3, -4), (-3, 4), (-2, 1), (2, -3), (3, -1).
- Here, the x-coordinate -3 is paired with both -4 and 4. Thus, a vertical line at x = -3 intersects the graph at two points. This set is **not** a function.
Therefore, the correct graph that represents a function is the one described in **option 2**.
Which graph shows a set of ordered pairs that represents a function?
On a coordinate plane, solid circles appear at the following points: (negative 5, 4), (negative 3, 2), (negative 1, 3), (1, 1), (1, negative 2), (3, negative 3).
On a coordinate plane, solid circles appear at the following points: (negative 5, 2), (negative 4, negative 4), (negative 3, 4), (negative 2, 2), (2, negative 2), (4, 3).
On a coordinate plane, solid circles appear at the following points: (negative 4, 2), (negative 1, 4), (1, 0), (2, 3), (2, negative 3), (3, 1).
On a coordinate plane, solid circles appear at the following points: (negative 4, 2), (negative 3, negative 4), (negative 3, 4), (negative 2, 1), (2, negative 3), (3, negative 1).
1 answer
1 answer