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Example 3 Determine whether each relation is a function.

x=15

Short Answer

Expert verified

The given relation is not a function.

Step by step solution

01

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.

02

Step 2. Concept Used.

  • The function is denoted asf:ABwhich 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.
03

Step 3. Explanation.

In the given relation x=15, observe that the graph of the relation is a vertical line. So, the vertical linex=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.

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