Answer:
A function is a relationship that maps the elements of a set, the domain, into elements of another set, the range.
The restriction that we have for functions is: The elements on the domain can be mapped into only one element in the range.
Then if:
f(x1) = y1
and
f(x1) = y2
where y1 is different than y2
f(x) is not a function.
Now, in the graph you can see a region where both lines overlap, then for some values of x we have two possible values of y, this means that the graph does not represent a function.
Then:
Ed: He is incorrect because we can have different values in the domain mapped into the same value in the range (like in the case of a line y = b, where we have all the elements in the domain mapped into the same element in the range, b)
Debra: There is something called piecewise functions, that are functions of this type, formed by different pieces.
Alejandro: He is correct.
Antoine: Not because you can write an equation means that the relation is a function. You can write an equation for a circle, but it will not be a function.
