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.
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.