Use the given graph to determine the limit, if it exists. -2; 6 1; 1 Does not exist; does not exist 6; -2

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Use the given graph to determine the limit, if it exists. -2; 6 1; 1 Does not exist; does not exist 6; -2

Mathematics
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Do you know how to evaluate f(2.1)?

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from looking at the graph
|dw:1438030387764:dw|
Imagine you're walking on the graph, towards x=2, from the right side : |dw:1438030518779:dw|
ok so what do i do next? @ganeshie8
what value does the graph takes as you approach x=2 ?
idk 2? @ganeshie8
careful, values down that horizontal axis are negative so i think you mean -2 ?
yes. so is that the final answer? -2? @
|dw:1438030838624:dw|
Yes, so we say the limit from right hand side of x=2 is \(-2\) and we write it mathematically as : \[\Large \lim\limits_{x\to2^{+}}~~f(x)~~~=-2\]
see if you can guess the limit from left hand side : \[\Large \lim\limits_{x\to2^{\color{red}{-}}}~~f(x)~~~= ?\]
would it be 6? @ganeshie8
Perfect! You do knw these things!
so the answer is -2;6 @ganeshie8
And if you notice f is approaching -2 if you plug in values to the right of x=2 like f(2.5)=-2 f(2.3)=-2 f(2.1)=-2 These numbers don't all usually appear the same but these numbers are approaching -2 as x approaches x=2 you can do the same thing for the left... also I know f(2.1)=-2 from just looking at: |dw:1438031090291:dw|
and also I probably could have drawn 2.1 closer to 2 but it is kind of hard to draw it closer to 2.1 without making it ugly and not readable

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