Which of the following rights is guaranteed by the Arizona Constitution?

The Arizona Constitution guarantees the right to free public education under Article 11, Section 1. This provision establishes the state's responsibility to provide for a system of public schools and emphasizes that education is a fundamental right for all children within the state. By ensuring access to free public education, the Arizona Constitution reinforces the idea that education is essential for an informed and engaged citizenry, which is critical for the functioning of a democratic society.

While other options, such as the right to privacy, the right to bear arms, and the right to free speech, may be addressed in various ways through amendments or interpretations of both the U.S. Constitution and Arizona law, the specific guarantee of free public education stands out as a clear and explicit right outlined within the Arizona Constitution itself. This distinction is what makes this option the correct choice in this context.