How can you determine if this equation: x-6=y2 is a function or not?

Determine if class="AM">`x-6=y^2` is a
function.

(1) If a relation is a function, each
input corresponds to exactly one output. If x is the independent variable, and y the
dependent variable, then this relation is not a function. The following ordered pairs
are in the relation: (6,0),(7,1),(7,-1),(10,2),(10,-2). Notice that the input 7 has two
outputs; i.e. 1 and -1. Likewise the input 10 has two outputs. If any input has more
than one output then the relation is not a function.

(2)
Draw the graph. If you pass a vertical line across the graph, then the relation is a
function if the line crosses the graph at no  more than 1 point. If the vertical line
cuts the graph twice or more times, the relation is not a
function.

src="/jax/includes/tinymce/jscripts/tiny_mce/plugins/asciisvg/js/d.svg"
sscr="-1,12,-5,5,1,1,1,1,1,300,200,func,sqrt(x-6),null,0,0,,,black,1,none,func,-sqrt(x-6),null,0,0,,,black,1,none"/>

Notice
that the vertical line x=7 crosses the graph at two points, so the relation is not a
function.

(3) Try to write the relation in "function" form;
i.e. y=f(x). Here solving for y yields class="AM">`y=+-sqrt(x-6)` . Notice that there are really two functions
here, the positive root and the negative root. But if this relation was a function, you
would just get one function when solving for y.