Question

The graph of a function never has two different points with the same x-coordinate because__

A. the graph of a function cannot be a straight line.
B. each input value is mapped to a single output value.
C. each input value is mapped to more than one output value.
D. the graph of a function is a vertical line.

Answer 1

B. Each input value is mapped to a single output value

Answer 2

Answer: option B. each input value is mapped to a single output value.


Justification:


A function (per definition) is an unambiguos rule that maps each input to a different output.


That means that a single input value cannot have two (or more) different images (output values of the function).


Then, the graph of a function cannot have two different points with the same x-coordinate.


For example, these two points (0,5) and (0,6) cannot belong to a same function, because that is relating the same input (0) to two different values (5 and 6) which is precluded by the definition of function.