Determine which of the rational functions given below has the following feature. x-intercept is 3 A. $f(x)=\frac{3 x-1}{x+9}$ B. $f(x)=\frac{x+9}{x-3}$ c. $f(x)=\frac{x+3}{x+9}$ D. $f(x)=\frac{x-3}{x+9}$

Step 1 ：The x-intercept of a function is the value of x for which the function equals zero. For a rational function, this occurs when the numerator equals zero (since anything divided by a non-zero number is zero). Therefore, we need to find which of the given functions has a numerator that equals zero when x=3.

Step 2 ：Let's substitute x=3 into each function:

Step 3 ：For function A: \(f(x)=\frac{3x-1}{x+9}\), substituting x=3 gives \(f_A = \frac{3*3 - 1}{3 + 9} = \frac{1}{3}\)

Step 4 ：For function B: \(f(x)=\frac{x+9}{x-3}\), substituting x=3 gives \(f_B = \frac{3 + 9}{3 - 3} = -\infty\)

Step 5 ：For function C: \(f(x)=\frac{x+3}{x+9}\), substituting x=3 gives \(f_C = \frac{3 + 3}{3 + 9} = \frac{1}{2}\)

Step 6 ：For function D: \(f(x)=\frac{x-3}{x+9}\), substituting x=3 gives \(f_D = \frac{3 - 3}{3 + 9} = 0\)

Step 7 ：From the results, we can see that only function D has a root at x=3, which means that the x-intercept of function D is 3. Therefore, function D is the one that has the feature described in the question.

Step 8 ：Final Answer: \(\boxed{D. f(x)=\frac{x-3}{x+9}}\)