Question

i know its not a function i just don't know how to explain why
{(–5, –5), (3, 10), (7, 14), (3, 9)}

Answer 1

A function is a set of ordered pairs in which no two ordered pairs have the same first number.
Since you have two ordered pairs with the same first number, it cannot be a function.

Answer 2

thanks :)

Answer 3

I think about a function as a relation having the distinction of no two-timing x values.
In the slang of "two-timing," no x is unfaithful to its y. If the x of 3 is paired with 10, then it would not "two-time" 10 and pair again with 9 and be a member of an ordered pair associated with a function. The x of 3 in this relation did "two-time" so the entire set of ordered pairs cannot be termed as a function.

Answer 4

A definition of a function is that "for every x, there is a unique y". For x=3, there are two y values, 10 and 9, so y is not "unique"