Is it possible for an input - output relationship to represent a function if two different inputs produce the same output? Explain

Question

Is it possible for an input - output relationship to represent a function if two different inputs produce the same output? Explain

Answer 1

Yes...Consider the easy function f(x)= 2, a function that is a horizontal line. 

 

But if you input the same x and get two different outputs, as you would if the equation were y² = x, this graph would not pass the Horizontal Line Test.  This can be seen because if you solve for y, you get y = ±√(x).  This tells you there are two output y-values for any non-zero x in the domain.