Somehow, I became confused about how to treat compound modifiers that are used not before a noun but elsewhere in a sentence. These are the compounds such as well-known and low-key. They are hyphenated when they appear before a noun: a well-known singer, a low-key diplomat.
But when they appear after a verb, say, I got it in my head that they didn’t need the hyphen. In fact, the convention, as explained in the Gregg Reference Manual, is that if the compound modifier is “in an inverted word order or an altered form, retain the hyphen.” (Gregg, 10th edition, Section 815b)
So the singer is known well; therefore, the hyphen appears when I write, the singer is well-known. The dog looks friendly, so the dog is friendly-looking. The purchase is one that is exempt from taxes, so the purchase is tax-exempt.
The corollary for this that if these hyphenated compound modifiers appear elsewhere in a sentence and serve another function, the hyphen is dropped, as Gregg points out. So I would write about an up-to-date report, but would write, Bring me up to date on the progress of the report. (Gregg, 10th edition, Section 815a)
Maybe I will be able to keep it straight from now on, but just in case, I am putting a sticky note on that section in my copy of Gregg.