Final answer:
The function y(x) = (9 - 5x)/(9 + 2x) has a vertical asymptote at x = -9/2 and a horizontal asymptote at y = -5/2.
Step-by-step explanation:
To find the vertical and horizontal asymptotes of the function y(x) = (9 - 5x)/(9 + 2x), we need to consider the values that make either the numerator or denominator become zero, as well as the behavior of the function as x approaches infinity. Vertical asymptotes occur when the denominator is zero, and there is no corresponding zero in the numerator. In the given function, setting the denominator equal to zero gives us x = -9/2. Therefore, there is a vertical asymptote at x = -9/2.
Horizontal asymptotes are determined by the end-behavior of the function as x value approaches infinity. To find a horizontal asymptote, we compare the degrees of the numerator and the denominator. Since both the numerator and the denominator are linear (and thus of degree one), the horizontal asymptote is found by dividing the leading coefficients. In this case, it is y = -5/2 as x approaches infinity.