The word "waver" is derived from the physical act of moving in a wave pattern. However, it most often indicates the psychological state of going "back and forth" between two options without being able to make a decision. Often too, a wavering person is filled with doubt. In contrast to this, a person who persists shows a sureness that is quite the opposite of the phenomenon of wavering. Among the options provided, this is the best option for an antonym.

When something is impeded, it is prevented from doing its activity. The word literally comes from the Latin roots meaning to place something on the foot. (The word "pedestrian" has the same "pede" in it.) An antonym for impede would express the activity of helping something on its way. Among the options provided, the best such word is "facilitate," meaning to make easier. The "facil-" prefix means easy, as in "facile."

The word "sanction" can have two meanings when it is used as a verb. On the one hand, it can mean to threaten with a penalty. On the other hand, it can also mean to approve. Luckily, none of the wrong answers are an antonym for the meaning of threatening with a penalty. Therefore, we must assume that it means to approve. In contrast to this, to "proscribe" can mean to outlaw or to forbid.

The word "transfer" literally means to carry across (as in carrying across a border). When someone transfers goods or money, he or she sends them to someone else (or to another place). In contrast to such conveyance, we could consider an antonym to be "to hold on to." The word "retain" means just this, namely to keep something in someone's own possession (instead of giving it).

When someone is said to "subsist" on something, he or she barely survives—only well enough to keep together his or her physical being. This comes from the old philosophical notion of subsistence, which indicates the basic existence of a being—though not necessarily implying any great flourishing. In contrast to this, "burgeoning" growth is great, fruitful growth. When something or someone is burgeoning, that thing is greatly flourishing. This is a good contrast to merely "subsisting."

The word "extol" means to praise. Several options among the answers are synonyms for this—"laud" and "acclaim". The word "disclaim" is not an antonym. It means to deny. This is not the opposite of praising, however. The word "deride" means to show contempt about something. It is related to "ridicule" and "ridiculous"—the idea being that "deriding" means to make fun of something.

When we put something "into jeopardy," we put that thing at risk. The verb "jeopardize" merely signifies the act of putting something into such a risky situation. The best contrast to this is to protect the thing. Among the options provided, only "preserve" has this sense of protecting in contrast to endangering the thing in question.

The most frequent use of "corroborate" is probably in the sense of a courtroom testimony "corroborating" the truth or falsity of some claim. Such corroboration helps to support the claim being made. Such evidence is the opposite of contradicting evident—i.e. evidence that seems to speak against the claim being made.

We often speak of divulging in the context of secrets that are divulged. This means that they were revealed. Surprisingly the word is related to "vulgar" which means the masses or the common people. When you divulge something, you tell it to everyone—even the "commoners." In contrast to this, when we conceal something, we "cover it up" or keep it from being known or seen.

The word "accost" does not have to do with the price of goods. Strangely enough, it comes from the Latin that literally means to be at the side of someone or something else. In English, it means to speak to in a strong and vigorous manner. Often, it is an aggressive kind of speech, confrontational in nature. The point for this question is that accosting is directly addressing something. In contrast to this, evading something is avoiding it, quite the opposite of dealing with something "head on."