If the topic of your speech is rock climbing and your specific purpose is to familiarize your audience with basic rock climbing equipment, then the general purpose of your speech is to inform.
An informative speech can be described as a kind of speech that informs you about a particular theory, event or action.
A speech that is written to inform familiarizes the audience with the concept or event that is the focus of the speech.
In the scenario mentioned in the question, the speaker is introducing the audience with the basics of rock climbing equipment. As the purpose of his speech is to just familiarize the basics of rock climbing equipment, we will say that the purpose or intention behind the speech of the speaker is to inform the audience.
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