How to Transition to Transparent

I was wondering if it is possible to make a mesh that transitions or has an ombre from a solid colour to translucence.

You can animate most material properties by moving the cursor over them and pressing (I) to make a keyframe. Then move to another frame, and change the property and press (I) again. Then it will change from the one setting to the other.
Transparent and translucent are different, though, but yes, you can animate all of these material properties.

You can use a gradient texture feeding the factor of a mix shader to transition from one type of material to another.

Not knowing the effect you are going for, I used an RGB node to emphasize that the same color was used for both diffuse and translucent parts. The lighting is a single spot aimed directly onto the slab.

Yes, you can:

I just used an image texture (with gradient from colour to transparency on it)

OP: your title says transparent, your question says translucent. Bonus!