Is the equation #x^2+y^2=4# a function?

1 Answer

Answer:

No - there is more than one #y# value for each #x# value in the domain.

Explanation:

Equations in the form of #ax^2+by^2=r^2# form circles.

#x^2+y^2=4=2^2# looks like this:

graph{x^2+y^2-4=0 [-7.023, 7.024, -3.51, 3.513]}

Is this a function? That is, does there exist a single #y# value for each #x# value in the domain? And the answer is no - for essentially all the #x# values (excepting #x=pm2#), there are two #y# values for each #x# value.

This is often called the "vertical line test" - if you draw a vertical line for any value of #x# in the domain, does the vertical line encounter no more than one #y# value. We can see that if we do that (such as draw a line along the #y# axis), we'll hit two #y# values.