SOLUTION: Are all linear equations function? Is there an instance when a linear equation is not a function? Support your answer.
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Question 189905: Are all linear equations function? Is there an instance when a linear equation is not a function? Support your answer. Answer by solver91311(24713) (Show Source):
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The following is the definition of a function:
The mathematical concept of a function expresses dependence between two quantities, one of which is known and the other which is produced. A function associates a single output to each input element drawn from a fixed set, such as the real numbers (), although different inputs may have the same output.
The highlighted phrase is the key to answering your question. All linear equations have the property that there is one and only one output (y value) for each input (x value) -- with one notable exception. That exception is the equation of a vertical line, . In the case of a vertical line, there are an infinite number of outputs for the single available input.
So, the short answer is no, not all linear equations are functions. Any linear equation of the form is a function if and only if . Note that in the above, it is perfectly ok for A to be zero -- a horizontal line is a perfectly good function, even if not a very interesting one.
