Determine whether or not the equation defines y as a function of x.

Question

y^2 = 5 - x^2.

A. Function

B. Not a function.

Answer 1

If you picture moving the -x² term to the left side of the equal sign you might recognize this as the equation of a circle with center at the origin and a radius = √5.

This circle does not pass the vertical line test, so it does not represent a function. What this means is that some elements in the domain of the relation are associated with two different elements in the range, i.e.there are x-values associated with two different y-values. For example, when x = 2, y = 1 or y = -1.

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