Question

How do you graph `f(x)=3/x` and then use the horizontal test to determine whether the inverse of f is a function?

Answer 1

See below:

Explanation:

Let's first graph `f(x)=3/x` .

It's sometimes easier to see and work with if we say that `y=f(x)`, giving:

`y=3/x`

We can plot a few points, such as:

`((x,y),(3,1),(-3,-1),(9,1/3),(-9,-1/3),(0,"undefined"))`

and it graphs as:

graph{3/x}

Inverse

Now let's find the inverse of the function. To do that, we switch `x` for `y` and vice versa, then solve for `y`:

`x=3/y`

`xy=3`

`y=3/x`

Is `y=3/x` a function?

We can use the vertical line test (for any given test line dropped vertically, it will intersect our graph in no more than one place) to show that this is indeed a function. I'll drop a couple of test lines to show:

graph{(y-3/x)(x-0y-2)(x-0y+3)=0}