Question

Example 3 Determine whether each relation is a function.

$x=15$

Short answer

The given relation is not a function.

Step-by-step solution

Step 1. function.

A function is defined as the relation between two sets that maps elements of the first to a unique element of the second set.

Step 2. Concept Used.

• The function is denoted as$f:A\to B$which shows that function f maps every element of set A to a unique element of set B.
• Vertical line test: The graph of any relationship is a function if it satisfies the vertical line test, which states that if at any point of the graph, we draw a vertical line, then it must intersect the graph at only one point.

Step 3. Explanation.

In the given relation $x=15$, observe that the graph of the relation is a vertical line. So, the vertical line$x=15$ will intersect the line at many points.

Since the relation does not satisfy the vertical line test, the relation is not a function.

Thus, the given relation is not a function.