Okay, since you're talking about a function key in combination with the F-keys (F8), you're probably talking about a laptop, yes?
Typical modern laptops have an S-Video out and a VGA-out, but both represent the "external" monitor. Your video card driver will have special software accessible via a tab on the display properties (right-click empty space on desktop, 'Properties', 'Settings', 'Advanced'). One of the tabs should allow display setup, and you can tell the PC which monitors are "attached", which are primary, whether to extend your desktop, etc.
The Fn-F8 or whatever combination probably corresponds to an icon on the keycap that looks like a filled monitor with a slash and an empty monitor. Pressing this combo usually cycles between up to 4 modes: (1) laptop screen only (2) external output only (3) both showing the same thing (4) both showing independent things
If you have support for (4), you can extend your desktop from your primary display (e.g. laptop screen) to your external display (e.g. TV).