AP Precalculus / Unit 1: Polynomial and Rational Functions
1.7 Rational Functions and End Behavior
Notes
For $\displaystyle r(x)=\frac{p(x)}{q(x)}$, compare degrees:
- Bottom degree larger: horizontal asymptote $y=0$.
- Equal degrees: $y=$ ratio of leading coefficients.
- Top degree one larger: a slant asymptote (found by division).
Practice
Horizontal asymptote of $\displaystyle \frac{6x^2+1}{3x^2-x}$:
$\displaystyle \frac{6}{3}$.
Horizontal asymptote of $\displaystyle \frac{x+4}{x^3}$:
Bottom degree is larger.
$\displaystyle \frac{x^2+1}{x}$ has which kind of end behavior asymptote?
$\displaystyle x+\frac{1}{x}$ behaves like $y=x$.
Ready for more? Take the Unit 1 test.