Determine the horizontal asymptotes of the following functions. Graph the function if you need to check your answer.
a. The function $f(x)=\frac{17+9 x}{3 x-5}$ has a horizontal asymptote at...
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Step 1 ：The horizontal asymptote of a rational function can be determined by comparing the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the x-axis (y = 0) is the horizontal asymptote. If the degrees are equal, the horizontal asymptote is the ratio of the leading coefficients. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

Step 2 ：In this case, the degrees of the numerator and denominator are both 1, so the horizontal asymptote is the ratio of the leading coefficients. The leading coefficient of the numerator is 9 and the leading coefficient of the denominator is 3.

Step 3 ：Therefore, the horizontal asymptote is at y = 9/3 = 3.

Step 4 ：Final Answer: The horizontal asymptote of the function \(f(x)=\frac{17+9 x}{3 x-5}\) is at \(y=\boxed{3}\).