Example: If then:

1. what is the image of [-2, 1] ?
2. find a closed set whose image is not closed

Note that this function is continuous. The image of the interval [-2, 1] is [1/5, 1]. In particular, the image of a compact set is compact.

To find a closed set whose image is not closed we must consider an unbounded set. Otherwise, a closed and bounded set is compact, and since the image of a compact set under continuous functions is compact, it is in particular closed again.

But if we look at the closed, unbounded set [0, ), we see that the image of that set under the above function is the set (0, 1], which is not closed.