SOLUTION:
Case: Functions
Required: State the option which is not true
Method:
A) A set of ordered pairs (x, y) for every x there is only one y.
The fundamental property of a function is that for a given input value , it can't have more than one output value.
The same is applicable here
You can consider X as the input value and Y as the output value that you get after performing a set of operations on X(i.e. function) and since X can't be same for 2 different values of Y , (i.e. the given condition) , it should be a function.
B) A vertical line most not intercept the graph of a function in more than one point.
If any vertical line intercepts the graph of a function at more than one point, the equation that corresponds to the curve is not a function
C) For every output, there is only one input
A function is a specific type of relation in which each input value has one and only one output value. An input is the independent value, and the output value is the dependent value, as it depends on the value of the input.
D) For every element in the domain there is only one element in the range.
A relation in which each element in the domain corresponds to exactly one element in the range is a function. A function is a correspondence between two sets where each element in the first set, called the domain, corresponds to exactly one element in the second set, called the range.
Final answer:
Option (C) is not always true. This is because of quadratic(or polynomial) equations that two inputs can result to one output.