College Algebra, Chapter 4, Chapter Review, Section Review, Problem 74

Analyze the graph of the rational function $\displaystyle r(x) = \frac{2x - 7}{x^2 + 9}$ by using a graphing device. Find all $x$ and $y$ intercepts and all vertical, horizontal and slant asymptotes. If the function has no horizontal or slant asymptote, find a polynomial that has the same end as the rational function.







Based from the graph, the $x$ and $y$ intercept is approximately $3.5$ and $-0.75$ respectively. Since the degree of the numerator is less than the degree of the denominator, then, the line $y = 0$ is the horizontal asymptote. Also, the zeros of the denominator is complex. So, the function has no vertical asymptotes.