# What is the limit for this function? [closed]

Is the limit for this function exist?

$\lim_{ x\to 3}$ for $f(x)=|2x-4|$

I think the limit for this function is $2$.

Is my answer correct or not? Because my teacher said there is no limit for this function. So I am confused

## closed as off-topic by vonbrand, Thomas, Shailesh, Leucippus, choco_addictedApr 5 '16 at 1:26

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• I dont see any reason why your answer should be wrong. The function is continous and the limit is well defined. – MrYouMath Apr 4 '16 at 16:30
• @MrYouMath that means my answer is correct, right? – Tony Apr 4 '16 at 16:33
• Yes, your answer is correct. – MrYouMath Apr 4 '16 at 16:34

So $|2x-4|$ does have a limit which exists as $x \to 3$.
A related statement that's similar to what you were told (except for the fact that this related statement is true) is that $|2x-4|$ doesn't have a derivative at $x=2$. Note that that's 2 and not 3.
Notice that $|2x-4|=2x-4$ when $x\ge2$ and then $$\lim_{x\to3}|2x-4|=\lim_{x\to3}(2x-4)=2(3)-4=2$$