Which statement describes how to determine if a relation given in a table is a function?

if none of the output values are repeated, the relation is a function.
if none of the input values are repeated, the relation is a function.
if any of the input values are equal to the output values, the relation is a function.
if all the output values are paired with the same input value, the relation is a function.

Definition: A function is a special relationship where each input has a single output.

Consider all options:

A. If none of the output values are repeated, the relation is a function.

Counterexample: given function y=|x|, for x=1 and x=-1, y=1. This means that output value can be repeated.

B.  If none of the input values are repeated, the relation is a function.

This is true option according to definition.

C. If any of the input values are equal to the output values, the relation is a function.

Counterexample: given function y=x, for all x  input value is the same as output value.

D. If all the output values are paired with the same input value, the relation is a function.

This option describes only function y=x, but is not true in general.

correct choice is B.

452,489 to the nearest thousand is 452,000

the answer

b. they are parallel and will never intersect.