# How do you find all the asymptotes for function f(x) = (7x+1)/(2x-9)?

That is when the numerator gets near to $0$:
$2 x - 9 \approx 0 \to x \approx 4 \frac{1}{2}$
The horizontal is found when we make $x$ larger and larger. The $+ 1$ and $- 9$ then matter less and less, and the funtion begins to approach $f \left(x\right) \approx \frac{7 x}{2 x} = \frac{7}{2} = 3 \frac{1}{2}$