Graphical limits

The complete graph of a function f is shown below. Referring to that graph, compute the following limits and values or explain why they don’t exist.

1. f(0)
2. \displaystyle \lim _{x\to 0}f(x)
3. \displaystyle \lim _{x\to 0^-}f(x)
4. f(1)
5. \displaystyle \lim_{x\to1}f(x)

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1) f(0) = 1
2) DNE because the limit approaches different values when coming from the left versus the right side.
3) \displaystyle \lim _{x\to 0^-}f(x) = 1
4) f(1) = 0
5) \displaystyle \lim_{x\to1}f(x) = 1

For question 5, shouldn’t the answer be 0?

No. The black dot indicates that f(1)=0 but f(x)\neq0 for other values of x close to 1. In fact, it looks like f(x) is close to 1 when x is close (but not equal) to 1,

Perhaps, this Desmos graph helps a bit. You can move the glowy black dot on the graph and its y-coordinate is always close to 1, when x is close to 1. It actually disappears if you try to put it right on that hole.