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Which of the following statements correctly describes the graph below?

Jensen, Tracey. Created for Albert.io. Copyright 2016. All rights reserved.

The function is not continuous at $x=1$.$ \lim _{ x\rightarrow 1 }{ f(x) } $ does not exist.$f(1)=1$

The function is continuous at $x=1$.$ \lim _{ x\rightarrow 1 }{ f(x) } $ does not exist.$f(1)=1$

The function is not continuous at $x=1$.$ \lim _{ x\rightarrow 1 }{ f(x) } $ exists.$f(1)=1$

The function is not continuous at $x=1$.$ \lim _{ x\rightarrow 1 }{ f(x) } $ does not exist.$f(1)=0.5$, and $f(1)=2$