I've witnessed recently a terrible trend in corporate culture that treats ask as a noun, as if I can pose an ask or request what an ask is, or, absurdly, ask what is their ask. This is stupid. We have a perfectly comfortable word that already performs the action in noun form: question. Turning ask into a noun not only confuses anyone used to its standard verb function, but also creates a redundancy, even if ask is a shorter word than question.
A good synonym should perform a similar function, not an equal function. Affect and influence are technically synonyms, but they imply different actions. Throw in impact as a synonym for both (a recent and bad trend in modern English), and you'll notice it does not perform anything that affect or influence don't already cover. School courses taught some of us to treat synonyms as equals. Swap a common word for an equal uncommon word and you pass that SAT essay. But this isn't true. Even words like glad and happy, which may have the same definition, imply different meanings. Happy conveys bright smiles and an extroverted cheerfulness, while glad speaks more softly—the person may not smile wildly or walk with a sprightly gait, but, if asked, would confirm he is in a positive mood. Bad synonyms, like impact (traditionally "to press closely into something") or, I fear, ask, add nothing new to our language. Allowing such words to infiltrate common speech and writing risks not only creating redundancies, but opening the door for habits that can devolve language into a mess of nonsense.
Language should remain as clean and forceful as it can, and inventing new definitions for already-grounded words does not help maintain linguistic strength. It may be interesting as a linguist, but not to a common speaker and writer. Confusing the definitions of words detracts from the cleanliness and forcefulness because it makes the reader understand known words in unknown contexts. I won't say language should stop evolving and all old word forms must remain and all new forms must die. This is stubborn and will, in the end, always fail (sorry prescriptivists). But the changes we do allow should be refreshing, inventive, and different. If a new word explains quickly something we could not before explain with ease, then it's fair game for adoption. Recent technology lends a perfect example: blog, smartphone, app all serve an exact function that before was not fulfilled by our language (online public diary page, handheld telephone that also acts like a computer, piece of software you can run). Language must evolve, but it doesn't need to evolve into redundancies and confusion.
Which brings me back to the nonsense of corporate English. Ask is a verb, question is a noun, and impact is a noun unless you mean to press closely, not to affect. Keep it that way. And when you find yourself in times of trouble, turn to this excellent cartoon for a reminder.