Question

Relations and Functions First, create your own response to the prompts below for numbers 1 and 2. Once you have posted your response, you are also required to respond to at least two other students' posts. You may want to check back later to respond to your classmates. 1. Make up two different relations consisting of a set of ordered pairs. Your set of ordered pairs should consist of 4 or 5 ordered pairs maximum. Make one of the relations a function, then make the other relation so it is not a function. Do not say which is which. Your classmates will determine this when they respond back to your post. 2. Explain how the vertical line test helps to determine whether or not a graph on a coordinate plane is a function or is not a function. For your original discussion post, you only need to respond to numbers 1 and 2.

Answer 1

1. Ordered Pairs

Relation A:
{(1, 2), (2, 3), (3, 4), (4, 5)}

Relation B:
{(1, 2), (1, 3), (2, 4), (3, 5)}

2. Explanation of the Vertical Line Test

The vertical line test is a visual method used to determine if a graph represents a function. According to this test, if any vertical line drawn on the graph intersects the curve at more than one point, the graph does not represent a function. This is because, for a relation to be a function, each input (or x-coordinate) must correspond to exactly one output (or y-coordinate). Conversely, if every vertical line drawn intersects the graph at most once, the graph does indeed represent a function. This test is simple and effective, allowing us to easily assess the nature of relations represented in a coordinate plane.