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

1 Answer
Jun 15, 2018

Answer:

#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#