Which of the following is the graph of a function where $y = f(x)$?
I got the answer for the above question is
A function has one output for each input in its domain. Each $x$-value on this graph corresponds to only one $y$-value. So the answer (c) is correct.
Can anyone explain the answer properly? I did not understand the answer from a single line.
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$\begingroup$In the first graph, if you take $x=1$, which $y$-value does it correspond to? If you draw a vertical line through $x=1$, that line hits two points on the curve. So there are two different $y$-values associated to $x=1.$ This contradicts the phrase in your answer "only one $y$-value." So (a) is not the answer.
If you can draw any vertical line and hit two or more points, then the picture is not the graph of a function.
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