# Sample quiz on rational functions with slant asymptotes Main home here.

1. Can a rational function have BOTH a horizontal asymptote and a slant asymptote?
A: Yes, always
B: Yes, sometimes
C: No, not possible
D: Not sure
2. If a rational function $\frac{p(x)}{q(x)}$ has a slant asymptote, then $\cdots\cdots$
A: the degree of $p(x)$ exceeds the degree of $q(x)$ by $1$
B: the degree of $q(x)$ exceeds the degree of $p(x)$ by $1$
C: the degree of $p(x)$ and the degree of $q(x)$ are equal
D: the degree of $p(x)$ exceeds the degree of $q(x)$ by $2$
3. The equation of a slant asymptote (of a rational function $\frac{p(x)}{q(x)}$) is usually $\cdots\cdots$
A: obtained by calculating the product $p(x)\times q(x)$
B: the remainder of the long division of $p(x)$ by $q(x)$
C: the quotient of the long division of $p(x)$ by $q(x)$
D: of the form $y=mx$ and is difficult to calculate.
4. Which of the rational functions below is NOT likely to have a slant asymptote?
A: $y=\frac{x^2-4}{x+3}$
B: $y=\frac{2x^2-x-1}{x+3}$
C: $y=\frac{x^3-1}{x^2-9}$
D: $y=\frac{x+1}{2x^2+5x+2}$
5. Find the equation of the slant asymptote of the rational function $y=\frac{x^2-9}{x+2}$
A: $y=x-2$
B: $y=x+2$
C: $y=x-5$
D: $y=-5$
6. What is the equation of the slant asymptote of the rational function $\frac{ax^2+bx+c}{x-2}$? (Assume $a,b,c\neq 0$)
A: $y=ax+b$
B: $y=a+bx$
C: $y=ax+(b+2a)$
D: $y=bx+(a+2b)$
7. If the line $y=2x-1$ is the equation of the slant asymptote for the rational function $\frac{2x^2+bx+5}{x-1}$, the value of $b$ is $\cdots\cdots$
A: $-3$
B: $-1$
C: $3$
D: $1$
8. Find the equation of the slant asymptote of the rational function $y=\frac{5x^2+2x+1}{3x+7}$
A: $y=\frac{5x}{3}-\frac{29}{3}$
B: $y=\frac{5x}{2}-\frac{29}{9}$
C: $y=\frac{5x}{2}-\frac{35}{9}$
D: $y=\frac{5x}{3}-\frac{29}{9}$
9. Find the equation of the slant asymptote of the rational function $y=\frac{x^2-4x+4}{x-3}$
A: $y=x-1$
B: $y=1-x$
C: $y=x+1$
D: $y=x-2$
10. Find the equation of the slant asymptote of the rational function $y=\frac{x^2-a^2}{x-b}$
A: $y=x+a$
B: $y=x-a$
C: $y=x-b$
D: $y=x+b$