What is the range of the given exponential function below? \( 3^{x}+2 \) \( (-\infty, \infty) \) \( (2, \infty) \) \( [2, \infty) \) \( (1, \infty) \)

To determine the range of the exponential function \( f(x) = 3^x + 2 \), let's analyze its behavior: 1. **Basic Exponential Function:** The function \( 3^x \) is always positive for all real numbers \( x \). Its range is \( (0, \infty) \). 2. **Transformation:** Adding 2 to \( 3^x \) shifts the entire graph upward by 2 units. Therefore, the new function \( 3^x + 2 \) will always be greater than 2. 3. **Limits:** - As \( x \) approaches \( -\infty \), \( 3^x \) approaches 0, so \( 3^x + 2 \) approaches 2 but never actually reaches it. - As \( x \) approaches \( \infty \), \( 3^x \) grows without bound, so \( 3^x + 2 \) also grows without bound. Combining these observations, the range of \( f(x) = 3^x + 2 \) is all real numbers greater than 2. **Correct Answer:** \( (2, \infty) \)