If we draw a curve of a function without drop the pen then the function must be continuous or not?I am confused with it. If there is curve for which some portion of the curve parallel to y axis at any any x then there have many value for single x and we can draw this curve without drop the pen then the curve is continuous or not?
2026-03-27 21:33:48.1774647228
Problem on concept of continuity
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The curve you drew is not even a function curve .To talk about the continouity you should have a well defined function .A function is said to be well defined from $\mathbb R $ into $\mathbb R $ if and only if , $\forall x,y\in \mathbb R$ if $x=y$ then $f(x)=f(y) $ which is not valid in your graph at $x=a$ .