Question

Does the equation below represent a relation, a function, both a relation and a function, or neither a relation nor a function?

y = x^2 - 4x

neither a relation nor a function
function only
both a relation and a function
relation only

Answer 1

Do you know the definition of a function and a relation?

"A function is a special relationship where each input has a single output.
It is often written as "f(x)" where x is the input value." - mathisfun.com/

"A relation between two sets is a collection of ordered pairs containing one object from each set. If the object is from the first set and the object is from the second set, then the objects are said to be related if the ordered pair is in the relation. A function is a type of relation." -mathinsight.org/

Answer 2

I would ask if it represents an explicit function.
An explicit function is the function that passes a "vertical line test". To pass a vertical line test, you have to have no x-coordinate repeat. Saying that at x=any number you have to have only 1 point, not more.

Answer 3

Some examples of failing a vertical line test.