Could someone explain why parts (a) and (b) are true? I initially thought that the limit does not exist (therefore false) but it turns out that the answer is true. I have been at this for a few days and I can't seem to figure out why.

Could someone explain why parts (a) and (b) are true? I initially thought that the limit does not exist (therefore false) but it turns out that the answer is true. I have been at this for a few days and I can't seem to figure out why.

If the graph really is as shown, then f(x) is not defined between -1 and 0 and so, yes, neither \(\displaystyle \lim_{x\to -1^+} f(x)\) nor \(\displaystyle \lim_{x\to 0^-}f(x)\) are defined.

If the graph is the line y= 1 for x between -1 and 0, then the limits would be as given.