Add views past date filter dropdown
The Date module has a submodule called Date Views that allows Views integration with Date fields.

Once enabled, you should be able to add an Exposed, Grouped filter on your date field. For each grouped filter, you can add your Label (e.g. "Past 7 days"), Operator (is between), &amp; Value which you can set to Relative dates that match your label (e.g. From: "-7 day" / To: "now").