Is #xy = 7 # a function?

1 Answer
Aug 4, 2015

If #x# and #y# are related by #xy = 7#, the #y# is a function of #x#.

Explanation:

Solve the equation for #y#.

We get #y = 7/x#

Now ask yourself: If I choose an #x#, do I ever get two different numbers for #y#? If the answer is NO, the #y# is a function of #x#.

In this case the answer IS no, so, #y# is a function of #x#.

For comparison

If #x# and #y# are related by #x+y^2 = 3#, then #y# is NOT a function of #x#.

When we solve for #y#, we get:

#y^2 = 3-x" "# so

#y = +-sqrt(3-x)#

Now, if I put in a number for #x#, I (usually) get TWO numbers for #y#. (except when #x=3#).
But if I EVER get two numbers (even just for one single solitary #x#) then #y# is NOT a function ox #x#.

So for #x+y^2 = 3#, we end up with: #y# is not a function of #x#.