Question

How do you use the vertical line test to show `x^2=xy-1` is a function?

Answer 1

`f(x)=x+1/x`

Explanation:

`x^2=xy-1`

Let's solve in terms of `y` so it is in standard function form:

`x^2+1=xy`

`x+1/x=y`

`y=x+1/x`

now is this a function, let's look at the graph:

graph{y=x+1/x [-10, 10, -5, 5]}

if you draw a vertical line anywhere across the domain of this graph (all `x` values) does it cross the graph twice? No, so this meets the criteria and is a function.

`f(x)=x+1/x`