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

214 Chapter 2 Polynomial and Rational Functions
47. fx
(a) Domain of f : all real numbers x except x 1
Domain of g: all real numbers x
(b) Because x 1 is a factor of both the numerator
and the denominator of f, x 1 is not a vertical
asymptote. f has no vertical asymptotes.
x2 1
, gx x 1
x 1
(c)
(d)
49.
x 2
fx
x
(a) Domain of f : all real numbers x except x 0 and
x 2
2 1
, gx
2x x
Domain of g: all real numbers x except x 0
(b) Because x 2 is a factor of both the numerator and
the denominator of f, x 2 is not a vertical asymptote.
The only vertical asymptote of f is x 0.
(c)
(d)
−4
−3
x 3 2 1.5 1 0.5 0 1
f x
gx
x 0.5 0 0.5 1 1.5 2 3
f x
gx
4
4
(e) Because there are only a finite number of pixels,
the utility may not attempt to evaluate the function
where it does not exist.
2
2
2
−2
1
−3
3
3
2.5
2.5
2
Undef. 2 1 Undef.
Undef. 2 1
3
Undef. 1.5 1 0
2
(e) Because there are only a finite number of pixels,
the utility may not attempt to evaluate the function
where it does not exist.
2
3
2
3
1.5
1
2
1
1
3
1
3
0
48. fx
(a) Domain of f : all real numbers x except 0 and 2
x2x 2
x2 , gx x
2x
2x 6
50. fx
x
(a) Domain of f : all real numbers x except 3 and 4
2 2
, gx
7x 12 x 4
Domain of g: all real numbers x except 4
(b) Since x 3 is a factor of both the numerator and the
denominator of f, x 3 is not a vertical asymptote
of f. Thus, f has x 4 as its only vertical asymptote.
(c)
(d)
Domain of g: all real numbers x
(b) Since x is a factor of both the numerator
and the denominator of f, neither x 0 nor x 2
is a vertical asymptote of f. Thus, f has no
vertical asymptotes.
2 2x
(c)
(d)
−2
−1
x 1 0 1 1.5 2 2.5 3
f x
(e) Because there are only a finite number of pixels,
the utility may not attempt to evaluate the function
where it does not exist.
x 0 1 2 3 4 5 6
f x
3
−3
2
−2
1 Undef. 1 1.5 Undef. 2.5 3
g(x) 1 0 1 1.5 2 2.5 3
1
2
1
2
2
3
8
1 Undef. Undef. 2 1
g(x) 1 2 Undef. 2 1
2
3
4
(e) Because there are only a finite number of pixels, the
utility may not attempt to evaluate the function where
it does not exist.