In your speech you decide to use a vivid and detailed narrative about a camping trip you took last year to illustrate one of your points about camping. This type of supporting material is called a(n) example.

The supporting material is called an extended example.

Explanation:

An extended example may be a narrative or way of supporting your argument in your speech. For instance, when you are telling a story and you need to strengthen or to reduce the complexity of some certain concepts. You can use a personal story or a narrative to strengthen and clarify your ideas, while in the same vein you are also making a personal connection with your audience.