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In this compound:enter image description here Will the parent chain be the one inside the loop, or the longer one including the single bonds to the left of the vinyl group?

I know that carboxylic acid is the highest-priority functional group, and that it must therefore be included in the parent chain. However, once we have selected a highest-priority group, don't the rest of the functional groups (in this case, a double bond) take on substituent priority? Therefore, I believe that the longer chain will be the parent chain in this case.

Is my attempt correct?

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You are quite right about the feeling that the longer chain must be the parent chain,

According to the newly revised (IUPAC Blue Book 2013), the longest chain containing the functional group regardless of presence unsaturation (here the double bond) will be the parent chain

Check this answer for details regarding this here

Hence the parent chain will be a 6-Carbon chain with the carbonic acid functional group. Therefore the correct Preferred IUPAC Name (PIN) will be 4‐methyl‐3‐methylidenehexanoic acid

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