1) Which of the following choices are rational functions? Check all that apply. A. $F(x)=\frac{6}{x^{2}}$ B. $F(x)=\frac{x+9}{x^{3}-4}$ C. $F(x)=\frac{3}{5 x}$ D. $F(x)=\frac{9}{x+1}$ E. $F(x)=\frac{x^{2}+\sqrt{x}}{x+7}$

Step 1 ：A rational function is a function that can be written as the ratio of two polynomials. The numerator and the denominator are both polynomials. The denominator cannot be zero.

Step 2 ：Looking at the options:

Step 3 ：$F(x)=\frac{6}{x^{2}}$ - This is a rational function. The numerator is a constant (which is a polynomial) and the denominator is a polynomial.

Step 4 ：$F(x)=\frac{x+9}{x^{3}-4}$ - This is a rational function. Both the numerator and the denominator are polynomials.

Step 5 ：$F(x)=\frac{3}{5 x}$ - This is a rational function. The numerator is a constant (which is a polynomial) and the denominator is a polynomial.

Step 6 ：$F(x)=\frac{9}{x+1}$ - This is a rational function. The numerator is a constant (which is a polynomial) and the denominator is a polynomial.

Step 7 ：$F(x)=\frac{x^{2}+\sqrt{x}}{x+7}$ - This is not a rational function. The numerator is not a polynomial because of the square root of x.

Step 8 ：Final Answer: The rational functions are A, B, C, and D. The function E is not a rational function.

Step 9 ：\(\boxed{\text{The rational functions are A, B, C, and D. The function E is not a rational function.}}\)