Example of a one-to-one function with required domain and range

Question

I missed a question on my last quiz and I don't get why.

"Draw the graph of a function which is one-to-one and has domain [-5,4) and range [-8,5]."

I didn't see how that is possible so I said "no such function" but I got marked wrong. He didn't tell me what the right answer is though.

Answer 1

It is possible to define a function which is one-to-one and has a half-open interval domain but a closed interval range. However, one of the simplest ways to do so uses an infinite number of line segments! Such functions are usually described only in university-level math courses with names like real analysis and set theory. I suspect your teacher made a mistake in stating the problem. But technically, he was correct that there is such a function.

Answer 2

Dewie, here’s a simple way to show such a function:

draw a straight line segment from (-5,-8) to (4,5).

This is a function because for every x-value, there is only one y-value.

The function is 1-1 because no two x-values have the same y-value

There are lots of other 1-1 functions on that domain and range, but this is one of them.

if you have any questions, please ask.