Question

Does the following relation represent a function? Why or why not? (-1,7) (-7,7) (17,7) (11,7)

Option 1: Yes, because it passes the vertical line test.
Option 2: No, because it has more than one output for the same input.
Option 3: Yes, because it has distinct x-values.
Option 4: No, because it has multiple x-values for the same output.

Answer 1

The relation given by the points (-1,7), (-7,7), (17,7), and (11,7) does represent a function because each x-value is paired with a unique y-value, and it would graph as a horizontal line, passing the vertical line test.

Step-by-step explanation:

The question asks whether the relation represented by the points (-1,7), (-7,7), (17,7), and (11,7) constitutes a function. A function is defined as a relation where each input (x-value) has exactly one output (y-value). In the given relation, each x-value is paired with the same y-value of 7. Despite having different x-values paired with the same y-value, this relation still represents a function because there is no x-value that is associated with more than one y-value. According to the vertical line test, if a vertical line intersects a graph at exactly one point, the graph represents a function. The relation in question would graph as a horizontal line at a positive value, which would pass the vertical line test, as every vertical line would intersect it at exactly one point.

Therefore, the correct answer to the student's question is Option 3: Yes, because it has distinct x-values.