The answer to your question is fill
The first purpose that Richard's soliloquy appears to serve is to reveal the motivations and personality of the character - we can see that he hates himself because he was basically a hunchback, so he was pretty self-conscious about it. He also reveals in the first scene what he intends to do throughout the play.
As for the second purpose, I'd choose the answer - it informs the audience about the background of the plot, as it gives us reasons why Richard decided to do what he did.
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Robert Browning's "My Last Duchess" does not rely heavily on metaphors. It is rather a monologue delivered by the speaker describing a painting of his wife and his wife as a person when she was still living. The painting can be said to symbolize the wife, the last duchess. There are a few metaphors sprinkled throughout the poem, though, as the speaker paints a verbal portrait of his former wife.
When the speaker says in lines 1-2 "That’s my last Duchess painted on the wall, / Looking as if she were alive," his choice of words could be considered metaphorical. The duchess herself is not literally on the wall; rather, this is a painting or a likeness of her, which stands in for her throughout the poem. One of the few metaphors in the poem is the "spot of joy" referenced by the speaker. The speaker suggests that most people wonder what exactly makes his lady smile and appear happy in the painting.
