Simply ignoring adverb phrases and prepositional phrases, however, will not be enough to allow us to distinguish all complements from all adjuncts. Under some conditions NPs and AdjPs can also be adjuncts. If we don't distinguish those adjuncts, we can misanalyze our sentences.
(18) My wife fed the dog freshly-cooked chicken.
(19) My wife fed the dog Tuesday morning.
In both (18) and (19), two NPs follow the verb fed. (18) is straightforward. The dog receives the chicken; we have a pattern of indirect object + direct object. On the other hand, if we try to fit (19) to the same pattern, things seem strange. Is Tuesday morning being fed to the dog? Clearly not. The other pattern with two NPs, VC, doesn't make much sense either. For that to work, Tuesday morning would be the object complement. But clearly that phrase isn't renaming the dog. Tuesday morning actually tells us when the action occurred. In other words, it is an adjunct, and fed in (19) is of type VT, with only a direct object as a complement.
If all this seems very intricate, don't despair. First, the better you know the basic patterns, the easier it will be to spot the unusual cases. Second, there is a relatively simple test to distinguish complements from adjuncts: do so substitution. The phrase do so, changed as necessary for the appropriate tense and number, can be used to replace a verb phrase and all its complements. It does not replace the adjuncts, however:
(18a) My wife fed the dog freshly-cooked chicken yesterday, and I did so today.
(19a) My wife fed the dog Tuesday morning, and I did so Wednesday evening.
(19b) *My wife fed the dog Tuesday morning, and I did so the cat.
In (18a), did so replaces the verb and both noun phrases (fed the dog freshly-cooked chicken). In (19a), it replaces fed the dog, but as (19b) shows it cannot replace fed in the morning, or even fed alone.
 Some verbs (e.g., put) do require certain prepositional phrases; strictly speaking, such prepositional phrases are actually complements rather than adjuncts. But since none of our verb subtypes involve prepositional phrases, you do not need to distinguish between PP complements and adjuncts for this course.
 In some grammar books, you will find verb-phrase adjuncts called adverbials. This label is meant to express the traditional notion that such prepositional phrases and other constituents function in the same roles that adverbs do, while keeping distinct the form (AdvP, PP, etc.) from the function (adverbial). Although the desire to distinguish form and function is sound, I don't use the term because in practice I have found that the similarity in form between adverb and adverbial produces continuing confusion.