To which family does the function \( y=(x+2)^{\frac{1}{2}}+3^{\text {belong? }} \) quadratic square root exponential reciprocal

The function given is: \[ y = \sqrt{x + 2} + 3 \] This function can be analyzed as follows: 1. **Quadratic**: These are functions of the form \( y = ax^2 + bx + c \). The given function does not involve an \( x^2 \) term, so it is not quadratic. 2. **Square Root**: This family includes functions that involve the square root of \( x \). The given function directly involves \( \sqrt{x + 2} \), fitting the square root family. 3. **Exponential**: These functions have the form \( y = a \cdot b^x \). The given function does not involve an exponent with \( x \) in the base, so it is not exponential. 4. **Reciprocal**: These are functions of the form \( y = \frac{1}{x} \). The given function does not involve a reciprocal of \( x \), so it is not a reciprocal function. **Conclusion**: The function \( y = \sqrt{x + 2} + 3 \) belongs to the **square root** family. **Answer**: square root