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

Jun 15, 2018

$f \left(x\right) = x + \frac{1}{x}$

#### Explanation:

${x}^{2} = x y - 1$

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

${x}^{2} + 1 = x y$

$x + \frac{1}{x} = y$

$y = x + \frac{1}{x}$

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.

$f \left(x\right) = x + \frac{1}{x}$