Example 3 Determine whether each relation is a function.

$y=3x-2$

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

• 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.

In the given relation $y=3x-2$, observe that the graph of the relation is a slant line increasing from left to right. So, the vertical line at any point of the graph will intersect the graph of the line at most once only.

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

Thus, the given relation is a function.