You may at least perform certain distortions, such as stretching, directly on the JPEG. This may depend on version.
And you may:
1) Create a rectangle fitting on top (you may use Smart Guides),
2) Select both and Object>Envelope Distort>Make with Top Object,
and distort freely.
The FreeTransform Tool works on raster images for ordinary scaling and rotation transformations.
The Free Transform Tool does not work on raster images for non-rectangular distortions (skewing, "perspective", etc), unless the image is embedded (not linked) and enclosed in an Envelope.
Therefore, you can:
1. Import the image.
2. Embed the image.
3. Object>Envelope Distort> Make with Mesh. Use 1 row and 1 column.
4. Use the FreeTransform with all its contortionist keyboard modifiers.
In Photoshop, you can do much the same kinds of distortions more easily using the Edit>FreeTransform or Edit>Transform>Distort or Edit>Transform>Perspective commands. See the Photoshop documentation.
One more thing: Why are you importing JPEGs to Illustrator? In case you don't know, JPEG is a lossy compression algorithm. Everytime you open a JPEG, modifiy it, and save it again as JPEG, you further degrade it unnecessarily. Don't do that. JPEG is for two things:
- Original input format from digital cameras. This is just an ugly, fact-of-life, necessary trade-off to make captured images small enough to deal with practically. (That's why, for images and uses worthy of higher discretion, better cameras provide support for capture in lossless TIFF or some raw format.) But if you intend to improve the captured image (which you should intend on any original capture), open the original capture in Photoshop and then forget about JPEG format. If the image is going to be placed in some other program for page assembly, incorporation into an illustration, or whatever, save the cleaned-up image from Photoshop in any appropriate LOSSLESS format, not JPEG.
- Final delivery to be manipulated no further. For print, final compression of finished CMYK image, not meant to be further manipulated by anyone. For web, final screen-res image, not scaled to any other "resolution" ready to be plopped into a web page with no scaling tags.
So in other words: As long as the progject is in progress, you should not be messing with JPEG format.