Show/hide affect object

The issue with motion effects is, that they always move relatively to the starting point. In your use case that starting point is moving!

You'll have to create two custom effects: one for easing in and one for easing out, both for the Text caption, which I will name Tx_Message. I will label those effects MoveIn and MoveOut

Create a tracking user variable (Boolean, only values 0/1) with a default value of 0. I will label it v_text.

Since the image has to be 'clickable', either you put that image into a shape that you convert to a shape button (step-by-step in this post: Turn an Image into a Button - Captivate blog).  Alternative is to put a click box over the image (you end up with two instead of one object). Be careful with the pausing point if you have other interactive objects on the slide.

Create a conditional advanced action to be triggered by the Success event of the shape button (or the click box):

IF v_text is equal to 0

   Apply Effect MoveIn Tx_Message

   Toggle v_text

ELSE

    Apply Effect MoveOut Tx_Message

   Toggle v_text

If you need this interactivity more than once, I recommend turning this advanced action to a shared action with Parameters the Effects and the Text Caption. The variable can be reused, has not to be a parameter. That way you'll be able to reuse the action, by choosing the effects and the caption on other slides.

TLCMediaDesign‌  Sorry, David, you seem to understand that the OP wants a Fade in effect, I understand with ease in/out that he meant a Motion effect with easing.

Not sure how you can do that with Captivate. I would think you would need 2 identical captions at the very least.

Very easy to do with jQuery animate. You could create an html page and zip it. Insert as HTML5 animation.

The basic syntax is fade in:

$('#your_caption').animate({opacity: 1,left: "+=100px",,0500);}

fadeout:

$('#your_caption').animate({opacity: 0,left: "-=100px",,0500);}

You would need to put these in functions and add a click handler to the image. With CSS, set the captions initial opacity to 0.