Math 111 Rational Functions Worksheet
For each of the following functions find the domain, y-intercept, x-intercept(s), holes, vertical asymp-
totes and horizontal asymptotes:
1. f(x) = x+ 1
x+ 2
2. g(x) = 3(xโ2)(xโ5)
(xโ2)(x+ 1)
3. h(x) = 1
x2
โxโ1
4. k(x) = x2
โ2xโ1
2xโ2
5. `(x) = 2xโ1
2x2
โ7x+ 3
6. m(x) = โ3(x2+ 2x+ 1)
4(x2
โ1)
7. s(x) = 5x2
โ20
3x2+ 12x+ 12
1. Give an example of a rational function pwhich satisfies all of the following properties:
(a) p(3) = 0
(b) p(2) is not defined
(c) phas a horizontal asymptote at y=1
3
2. Give an example of a rational function qwhich satisfies all of the following properties:
(a) q(8) = 0
(b) qhas a hole at x= 4
(c) qhas a horizontal asymptote at y= 0
3. Give an example of a rational function Rwhich satisfies all of the following properties:
(a) Rhas a zero at x= 2
(b) Rhas a hole at x= 3
(c) Rhas a vertical asymptote at x= 4
(d) Rhas a horizontal asymptote at y=โ
2
3
4. Give an example of a rational function which has no holes or vertical asymptotes and a hori-
zontal asymptote at y= 0.
