Not every relation is a function. But every function is a relation. Function is just a part of relation.
The cubic function.
Range
A formula or graph are two ways to describe a math function. How a math function is described depends on the domain of the function or the complexity of the function.
The Mandelbrot graph is generated iteratively and so is a function of a function of a function ... and in that sense it is a composite function.
Withal I am Here to save the day
The girls were really happy on getting an A+, withal finding their lost puppy.
To use as 'fish bait'.
Withal is now an obsolete word because its work has been taken over entirely with the word "with". An example from As You Like It: Rosalind: By no means, sir. Time travels in divers paces with divers persons. I'll tell you who Time ambles withal, who Time trots withal, who Time gallops withal, and who he stands still withal. Or from Merchant of Venice, when Shylock is asked what good the pound of flesh would be, he replies: To bait fish withal. In both cases, substituting the word "with" works perfectly in a more modern idiom. It would appear that Shakespeare did not like the sound of the preposition "with" at the end of the sentence and replaced it with "withal" in that position. (Many much more modern English speakers object to ending sentences with a preposition and recommend reversing the word order, with results which are sometimes amusing: "That is something up with which I will not put.") Shakespeare was, however, really fond of this word and used it in other contexts where its meaning is not so clear. E.g. Portia talking to the Prince of Morocco: The one of them contains my picture, prince: If you choose that, then I am yours withal. The word seems to add nothing except the two syllables necessary to round out the line. The same can be said of this line of Valentine's from The Two Gentlemen of Verona: These banish'd men that I have kept withal Are men endued with worthy qualities Possibly these uses of the word suggest "with" and an unspecified object which we have to get from context. So Portia's line means that she is the Prince's with something, perhaps the picture or perhaps her wealth. Valentine's banished men have been kept with him, presumably. The OED lists some examples where the word clearly means "with all the rest" which may be the kind of meaning here. Shakespeare uses this irritating word over 150 times.
Benvolio
personification. It is giving human-like qualities to something non-human.
He was exuberant when he won the lottery.He was a man of exuberant fancy, and, withal, of an authority so irresistible that, at his will he turned his varied fancies into facts.
withal. withdraw. withdrawal. withdrawer. withdrawn. withdrawnness. withe. wither. withered. withering. witheringly. withers. withhold. withholder. within. without. withstand. withstander. withy. withholdwithstand
He was a man of exuberant fancy, and, withal, of an authority so irresistible that, at his will, he turned his varied fancies into facts. - The Lady, Or the Tiger? by Frank R. Stockton
Nevertheless, still, yet, though, nonetheless, in spite of, despite that, conversely, on the other hand, but, after all, be that as it may, anyhow, for all that, howbeit, notwithstanding, per contra, withal, without regard to.
Nevertheless, still, yet, though, nonetheless, in spite of, despite that, conversely, on the other hand, but, after all, be that as it may, anyhow, for all that, howbeit, notwithstanding, per contra, withal, without regard to.
after all, all the same, anyhow, be that as it may, but, despite, for all that, howbeit, in spite of, nonetheless, notwithstanding, on the other hand, per contra, though, withal, without regard to, yet