C H A P T E R 2 Polynomial and Rational Functions

2 x x 2
7. fx
2 x x 2
Domain: all real numbers except x 2
11.
Vertical asymptote:
Horizontal asymptote: y 1
Degree of Nx degree of Dx
fx
Domain: All real numbers. The denominator has no real
zeros. [Try the Quadratic Formula on the
denominator.]
3x2 1
x2 x 9
Vertical asymptote: None
Horizontal asymptote: y 3
Degree of Nx degree of Dx
13. fx
Vertical asymptote: y 3
2
x 3
Horizontal asymptote: y 0
Matches graph (d).
x 2
9. fx
Domain: all real numbers except x ±1
x3
x2 1
Vertical asymptotes:
x ±1
Horizontal asymptote: None
Degree of Nx > degree of Dx
16.
x 2
f x
x 4
Vertical asymptote: x 4
Horizontal asymptote:
Matches graph (b).
y 1
12.
14. fx
Vertical asymptote: x 5
1
x 5
Horizontal asymptote:
Matches graph (a).
8.
fx
Section 2.6 Rational Functions 207
Domain: all real numbers except
Vertical asymptote:
Horizontal asymptote: y
Degree
of Nx degree of Dx
5
x
2
1
x
2
1
2
fx
Domain: All real numbers. The denominator has
no real zeros. [Try the Quadratic Formula
on the denominator.]
3x2 x 5
x2 1
Vertical asymptote: None
Horizontal asymptote: y 3
Degree of Nx degree of Dx
y 0
1 5x 5x 1
1 2x 2x 1
10. fx
Domain: all real numbers except x 1
2x2
x 1
Vertical asymptote:
17. gx
The only zero of gx is x 1.
x 1 makes gx undefined.
x2 1 x 1x 1
x 1 x 1
x 1
Horizontal asymptote: None
Degree of Nx > degree of Dx
15.
x 1
fx
x 4
Vertical asymptote: x 4
18.
Horizontal asymptote:
Matches graph (c).
hx 2 5
x 2 2
2 5
x 2 2
2x 2 2 5
x2 5
2
2
y 1
0 2 5
x 2 2
No real solution, hx has no real
zeros.