Question

Examples 1 and 3 Determine whether each relation is a function. Explain.

Short answer

The given relation is not a function.

Step-by-step solution

Step 1. Domain and range of a function.

In a function domain is the set of input (x) values and the range is the set of output (y) values.

Step 2. definition of the function.

A relation is said to be a function of each element in the domain of the relationship that has a unique value in the range. That is, no element in the domain has more than one value in the range.

Step 3. Alternative method.

By observing the above graph, at single input, we have two output values.

Draw a vertical line anywhere on to graph, then the line intersects at more than one point.

So, the vertical line test fails.

Therefore, a given relation is not a function.