A function cannot have any value of x mapped to more than one vaue of y. So, if any line parallel to the y-axis meets the graph at more than 1 points it is not a function.
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If you are looking at a graph and you want to know if a function is continuous, ask yourself this simple question: Can I trace the graph without lifting my pencil? If the answer is yes, then the function is continuous. That is, there should be no "jumps", "holes", or "asymptotes".
i need to know how to function rule and a sketch of a graph
One way is to try the vertical line test on a graph!
the graph is called a line
A sine graph!