Question

Determine whether each relation is a function.

$y=3x+2y$

Short answer

The given relation is 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 equation or relation is a function if it satisfies the vertical line test, which states that if at any point of the graph, draw a vertical line, then it must intersect the graph at any one point.

Step 3. Explanation.

In the given relation $y=3x+2y$, it can be simplified as $y=-3x$. Observe that the graph of the relation is a slant line decreasing 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.