How does the FB "Send" button choose which page image to send?

After clicking the FB Send button on an article page, how does the JFBC component select which page image is used in the pop-up box? I know the description is the meta-description added at the article level, but don't understand exactly how the image is selected, or how I can control which one is used by the component. Sometimes I will see an option under the image to scroll through several that are available on the page, but other times I only see one specific image when there are others on the page. How do I specify and control the image I want to be sent every time the button is used?
Thanks!

Thanks for the clarification -- I'm still a bit confused, however.

We are using RSSeo! for our SEO component. You can see from the first image attached what we have defined in the RSSEO Component for the Page Title and Meta Description. The second image is what displays when trying to use the Send button, which is still the default info.

If we define the RSSeo Page information in that component BEFORE we ever click the Send button a web page, the info displayed in the Send box is the correct information. If we happen to click the Send button on a web page before DEFINING the info in the RSSeo component, the component grabs the system default information and populates the Send box with it.

We have several pages where we have clicked the Send button prior to defining the Title and Description info in the RSSeo component, and now are stuck with the default information displaying similarly to the 2nd image, above.

If the insertion of your previously stated Tags will remedy the problem, that's great. We need a bit of guidance on exactly how to insert those tags in the articles...do we need a joomla component or plugin, ideally? or is there a simple way to just do it through the JCE editor we are using?
Thanks!

FB Debug tool...worked perfect, thanks.

As for "running the AutoTune to ensure our Domain is in the FB App correctly", I'm not exactly sure how to set it up to get what we want. The joomla instance is on IP 199.XX.XXX.XX in our data center. The domain is at GoDdady with A-record pointed to that IP address (we obviously want the browser address bars to show the domain name and not the IP address for all the web pages).

Should the FB App be populated with the domain name then, or the IP address instead...? (right now, we have the domain name in the FB app). When running AutoTune, its recommended settings use the IP address in order to get "green" returns on all the checks).

Don't we ideally want the domain name showing in both the JFBC component and the FB App? ...or does it even matter if the IP is used in both, instead?

Again, we just need to ensure the domain name shows in the address url of each page instead of the IP address, and that if we do have to use IP address for both JFBC and FB app settings, that doing this will not adversely effect Search Engine returns because the IP address is being used instead of the domain name.

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Lastly, we're having trouble getting the Open Graph tags to override the default settings to show the preferred image in Articles.

Example: We open an Article in joomla, click the JCE editor button that toggles to show the Source Code of the article, then insert the following tag at the end of the page: {SCOpenGraph image=http://graysonallen.com/images/diamond_only.jpg}. Save the Article, use the FB Debug tool to force the change, refresh the web page and click the FB Send button....the result still shows the default image, not the one specified in the Tag.

Note: the image in the above example in the joomla image library and is NOT part of the Article, does this matter? We have tested using images that are included in the Article but still have no luck. Maybe our method of adding the tag is not correct?

Thank you.