Question 656751
<pre>
y² = 7x

It is not a function because, for instance,

(7,7) and (7,-7) are both solutions, since:

(7)² = 7(7)
  49 = 49

But also

(-7)² = 7(7)
   49 = 49

In a function the same value of x cannot correspond 
to two different values of y.

However, (7,7) and (7,-7) have the same x-values 
but different y-values.

Also the graph of y² = 7x is this:

{{{drawing(200,200,-5,5,-5,5,
graph(200,200,-5,5,-5,5,sqrt(7x)),
graph(200,200,-5,5,-5,5,-sqrt(7x)) )}}}

And it does not pass the vertical line test, because
these vertical lines (in green) intersect the graph
in two places, which a function cannot have.

{{{drawing(200,200,-5,5,-5,5,
graph(200,200,-5,5,-5,5,sqrt(7x)),
graph(200,200,-5,5,-5,5,-sqrt(7x))   ,
green(line(2.3,10,2.3,-10),line(3.2,10,3.2,-10),line(.6,-10,.6,10))  ,
circle(2.3,sqrt(7*2.3),.3),circle(2.3,-sqrt(7*2.3),.3)  ,
circle(3.2,sqrt(7*3.2),.3),circle(3.2,-sqrt(7*3.2),.3)   ,
circle(.6,sqrt(7*.6),.3),circle(.6,-sqrt(7*.6),.3) 


 )}}}

Edwin</pre>