Of the various types of syntax, functional syntax is not very popular. In fact, the study of functional syntax is less common today than it used to be. It probably reached its height of popularity in the 1970's. Nevertheless, it is useful for analyzing the function of phrases in sentence structure.
I will illustrate the use of functional syntax with infinitive clauses. The bare infinitive consists of a verb as in "I must go" and "They can come". In both examples, the infinitive is preceded by a modal. In other cases, though, the infinitive consists of a particle, "to" and a verb. This is illustrated in the example "Oliver needs to study." Here the infinitive consists of "to study". This infinitive can be classified as a clause consisting of a particle and a verb but the infinitive clause can be expanded as in the following examples: "Oliver needs to study more", "Oliver needs to study math", and "Oliver needs to study because he has an exam tomorrow".
Now let us consider the different functions of infinitive clauses. The following sentence is a famous one: "To err is human". In this sentence the infinitive clause is "To err". It has a nominal function because it can be replaced with the pronoun "It." In the sentence "I want to eat now", the infinitive clause "to eat now" also has a nominal function because it can be replaced by the pronoun "it". In the sentence "To graduate in one year is Martina's goal", the infinitive clause "To graduate in one year" also has an nominal function.
In the sentence "Erik Frost is the man to lead our company", the infinitive clause "to lead our company" has an adjectival function. It describes the kind of man that Erik Frost is. In the sentence "The best way to remain healthy is a good diet and regular exercise", the infinitive clause "to remain healthy" has an adjectival function because it modifies the noun "way".
Infinitive clauses can also have an adverbial function. Consider the sentence "Richard is taking Chinese this semester to prepare for his trip to China". The infinitive clause "to prepare for his trip to China" has an adverbial function because it modifies the verb "taking" and also answers the question "Why is Richard taking Chinese this semester?". In the sentence "Paul is too sick to go out", the infinitive clause "to go out" also has an adverbial function because it modifies the adjective "sick". It functions as an adverb also known as a degree word such as in the examples "so hot", "very tired" and "really windy".
Functional syntax is a type of syntax which is rarely studied today. Despite its relative obscurity, it can be very useful for the study of the function of different elements of sentences. One example is the study of the different functions of infinitive clauses.