Question
To which family does the function \( y=(x+2)^{\frac{1}{2}}+3^{\text {belong? }} \) quadratic square root exponential reciprocal
Ask by Allan Nguyen. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The function \( y = \sqrt{x + 2} + 3 \) belongs to the square root family.
Solution
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
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
The function \( y=(x+2)^{\frac{1}{2}}+3 \) belongs to the square root family. This is because it involves the square root of a linear expression \( (x+2) \), indicating that the function's graph will display the characteristic shape of a square root function, starting from its vertex at \( (-2, 3) \). In terms of its real-world application, square root functions can often model situations where a quantity grows at a decreasing rate. For example, the distance traveled by an object under the influence of gravity can be represented by a square root function as it falls, making it valuable in physics and engineering contexts.
