None of the sentences provided in your options contain a prepositional phrase. A prepositional phrase typically includes a preposition followed by a noun or noun phrase.
Here's a brief overview of the options:
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"I walked the dog after I cleaned my room." - The phrase "after I cleaned my room" is a dependent clause, not a prepositional phrase.
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"I think Sarah crossed the finish line first." - The phrase "across the finish line" contains a preposition ("across"), but it is not the correct form in this context since the sentence doesn't use "crossed" in the prepositional sense.
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"Joe is going to swim and then go home." - The phrase "go home" does not contain a prepositional phrase.
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"My science project examines the planet Mars." - This sentence does not include a prepositional phrase either.
Please check to ensure there are prepositional phrases in your options, as it might seem like they are not present in the provided sentences.