Answer
Yes.
Work Step by Step
One way to know whether a function is one-to-one is by using the horizontal line test. Sketch the graph manually or with the use of a graphing calculator. A horizontal line drawn anywhere on the graph does not intersect the function twice. Therefore, the function passes the horizontal line test and is a one-to-one function.
$y=\frac{-1}{x+2}$ is a one-to-one function.
