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Answer:
Function Definition
Step-by-step explanation:
The equation in two variables x and y is considered a function if each value of xx corresponds to exactly one value of y. In this context:
Function: An equation y=f(x)y=f(x) is a function if, for every input xx, there is a single output y. This means that for each value of xx, there should be only one corresponding value of y, ensuring that y is uniquely determined by xx.
Example: In the equation y=2x+3y=2x+3, for each value of xx, there is a unique value of y. Thus, this equation represents a function.
Non-Example: In the equation x2+y2=1x2+y2=1 (the equation of a circle), for some values of xx, there are multiple corresponding values of y. For instance, if x=0x=0, y can be 11 or −1−1. Therefore, this equation does not define y as a function of xx.
In summary, for an equation y=f(x)y=f(x) to be a function, each xx value must correspond to exactly one y value, ensuring a clear, one-to-one relationship between the variables.