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Gradient Mask in Illustrator
One of the handy little things you can do with your vector graphics in Illustrator, is create areas of transparency, just like in Photoshop, using a mask. Illustrator lets you add opacity masks where you can use one shape to mask another. If the masking shape is filled with a gradient, white to black, the white areas will be 100% opaque and the black areas will be 100% transparent. All the shades in between will give you the smooth fade effect.
You need to make sure you have 2 objects for this:

Target Object
Your target object and your mask shape.

Mask Shape
The mask needs to be directly above your target layer in the layers palette.

Layers Palette
Select both objects by either shift + clicking on them or dragging a selection to cover them both.
Open your Transparency Palette (Window > Transparency) and click the disclosure triangle to reveal a drop-menu.

Transparency
Select Make Opacity Mask and voila!

Masked Result
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