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:
So in other words: As long as the progject is in progress, you should not be messing with JPEG format.