1. The problem states that the function $f$ is composed of two pieces: a polynomial piece and an exponential piece. 2. The graph shows the polynomial piece on the left side for $x < -2$ and the exponential piece on the right side for $x \geq -2$. 3. The domain of the exponential piece is where the exponential part of the function is defined, which is from $x = -2$ onwards. 4. This means the exponential piece's domain is $x \geq -2$. 5. Among the given options, the inequality that represents this domain is $x \geq -1$ is incorrect, $x > 1$ is incorrect, $x > 3$ is incorrect, and $x \leq -2$ is incorrect. 6. The correct inequality is $x \geq -2$, but since it is not listed exactly, the closest correct option is $x \geq -1$ which is not correct for the domain. 7. Therefore, the correct answer based on the graph and description is $x \geq -2$, which matches the exponential piece's domain. **Final answer:** The domain of the exponential piece is $x \geq -2$.