AP Precalculus / Unit 1: Polynomial and Rational Functions
1.8 Rational Functions and Zeros
Notes
The zeros of a rational function are the real zeros of the numerator that are not also zeros of the denominator.
- Sign charts use zeros and vertical asymptotes to find where $r(x)>0$ or $<0$.
Practice
Zeros of $\displaystyle \frac{x^2-9}{x+3}$:
$x=-3$ makes the bottom 0, so it's a hole, not a zero.
Zeros of $\displaystyle \frac{x-5}{x^2+1}$:
The bottom is never 0.
On a sign chart, the sign of a rational function can change only at:
Those are the breakpoints.
Ready for more? Take the Unit 1 test.