Question

How do you graph the function `f(x)=3` and its inverse?

Answer 1

`f(x)=3` has a graph which is a horizontal line. The inverse relation (not a function) has a graph which is a vertical line.

Explanation:

The graph of `f(x) = 3` is a horizontal line `y=3` through `(0, 3)`...

graph{y=3+0.000001x [-10, 10, -5, 5]}

To obtain the graph of the inverse, we can reflect this graph in the diagonal line `y=x` to get:

graph{x=3+0.00001y [-10, 10, -5, 5]}

If that does not look like the graph of a function to you, that's probably because it isn't. The only value of `x` for which there are any values of `y` is `x=3` and then there are an infinite number of values to choose from.