In the sentence "My dog insists that I throw the tennis ball," the verb mode used is the subjunctive. The subjunctive mode is being expressed in the clause "that I throw the tennis ball."
- Demand or recommendation: The subjunctive mood often expresses demands, recommendations, or wishes. In this case, the dog's insistence can be interpreted as a demand for you to throw the tennis ball.
So, the correct answer is: one subjunctive, a demand or recommendation.