\( \begin{array}{ll}\text { 5. } f(x)=3 x^{2} & \text { 6. } f(x)=-x^{2}+1 \\ \text { 7. } f(x)=-x^{2}+4 x+1 & \text { 8. } f(x)=\frac{1}{2} x^{2}+6 x-7 \\ \text { 9. } y=(x+1)^{2} & \text { 10. } f(x)=(2 x-5)^{2} \\ \text { 11. } f(x)=x^{3}+x & \text { 12. } f(x)=2 x^{3}+x^{2} \\ \text { 13. } y=-x^{3}+15 x^{2}-x & \text { 14. } y=3 x^{4} \\ \text { 15. } y=\frac{2}{x+1} & \text { 16. } y=\frac{x}{x-1} \\ \text { 17. } y=\frac{2 x+3}{x+4} & \text { 18. } f(x)=\frac{1}{x}+\frac{1}{x^{2}} \\ \text { 19. } f(x)=\frac{1}{4} & \text { 20. } f(x)=\sqrt{2 x+1}\end{array} \)

It looks like you've provided a list of functions, possibly for analysis or evaluation. If you have specific questions or tasks related to these functions, such as finding their domains, ranges, intercepts, or any other properties, please let me know! Here are some general observations about the types of functions you've listed: 1. **Quadratic Functions**: - Functions 5, 6, 7, 8, 9, and 10 are quadratic functions. They can be analyzed for their vertex, axis of symmetry, and intercepts. 2. **Cubic Functions**: - Functions 11, 12, and 13 are cubic functions. They can have one or two turning points and can be analyzed for inflection points. 3. **Polynomial Functions**: - Function 14 is a quartic function, which can have up to three turning points. 4. **Rational Functions**: - Functions 15, 16, 17, and 18 are rational functions. They can have vertical and horizontal asymptotes, and their behavior can be analyzed as \( x \) approaches certain values. 5. **Constant Function**: - Function 19 is a constant function, which has a horizontal line as its graph. 6. **Square Root Function**: - Function 20 is a square root function, which has a domain restriction (it must be non-negative). If you need specific analyses or evaluations for any of these functions, please specify!