Ah ok. I already tried both CloudDeploy[f] and the ?Website= and I could not get it to work. I'm glad that you told me that it was broken. Again, thanks for taking your time to explain it to a newbi like me.

Import HTML images

Deploy and test Sean Clarke's API:

With[{cloudobject = FileNameJoin[{$CloudRootDirectory, "ImportHTMLImageAPI"}]},
   CloudDeploy[
      APIFunction[{"Website" -> "SemanticURL"}, First@Import[#Website, "Images"] &, "JPEG"],
      cloudobject, Permissions -> "Public"];
   URLExecute[URLBuild[cloudobject, {"Website" -> "google"}]]]

For the above query "google" the API returns:

Eventually, a better solution might be to import HTML images from a private cloud.

Update 12/18/15

Previous update on 12/14/15 confirmed Sean Clarke's API was working, but the CloudObject had default "Private" permissions, which works fine from a browser signed into the Wolfram Development Platform, but gives an signin error from URLExecute.

The second argument to APIFunction should be a function. The most common way to give the function is as a pure/anonymous function. To make a pure/anonymous function, you are missing the apersand:

f = APIFunction[{"Website" -> <|"URL" -> "String"|>}, Import[#Website, "Images"] &]

f[<|"Website" -> "http://www.google.com"|>]