Question

The following images all include inverse relations of different functions.

Which images show an inverse relation that is also a function?

Select all that apply

Answer 1

Answer: The First Graph and the Last Graph

Explanation:

So all of these are inverses of a function. But as for how do you tell if the inverse is a function...

Well, it has to pass the test that all functions have to pass: the Vertical Line Test.

Any time you draw a vertical line down a graph, it should ONLY PASS THROUGH ONE POINT.

Your pictures are a little blurry, but as far as I can tell, Graph 1 is pretty linear, and a vertical line drawn would only intersect one point on the graph.

The second one however... well it seems pretty obvious why the vertical line test wouldn't work there. A vertical line drawn on the right half would intersect two points, which does not pass the test.

Same thing for Graph 3.

Graph 4 looks like it would pass the vertical line test. I cannot see the section on the y-axis that well, but it looks like it doesn't double back on itself.

Just check them with the Vertical Line Test! It's really useful for figuring out if something's a function or not.