Question

Determine whether each relation is a function.

Short answer

The given relation is a function.

Step-by-step solution

Step 1. Definition of 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.

A function is defined as the relation between two sets that maps elements of the first to a unique element of the second set. And it 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, observe that the graph of the relation is an upward-opening parabola. Also, observe that the vertical line at any point of the graph will intersect the graph of the parabola at most once only.

Since the relation satisfies the vertical line test, the relation is a function.

Thus, the given relation is a function.