72 27.
Chapter 2 f ( x) =
3x 3x = x 2 − x − 2 ( x + 1)( x − 2)
33.
f ( x) =
2+ x x+2 =− 1− x x −1
Vertical asymptote: x = 1 Horizontal asymptote: y = −1
Intercept: (0, 0) Vertical asymptotes: x = −1, 2 Horizontal asymptote: y = 0
Domain: x ≠ 1 or (−∞, 1) ∪ (1, ∞) 35.
−3 0 3 4 1 9 3 9 6 y − 0 − 10 2 4 5 x 2 + 3x x( x + 3) x f ( x) = 2 = = , x + x − 6 ( x − 2)( x + 3) x − 2
Domain: t ≠ 0 or (−∞, 0) ∪ (0, ∞)
x ≠ −3 Intercept: (0, 0) Vertical asymptote: x = 2 (There is a hole at x = −3. ) Horizontal asymptote: y = 1
37. h(t) =
y
31.
f ( x) =
−2 −1 1 1 2 3
4 t2 + 1
Domain: all real numbers or (−∞, ∞) Horizontal asymptote: y = 0
39. x
3t + 1 t
Vertical asymptote: t = 0 Horizontal asymptote: y = 3
x
29.
f (t ) =
0
1
2
0
−1 Undef.
3 3
x 2 − 1 ( x + 1)( x − 1) = = x − 1, x +1 x +1
x ≠ −1 The graph is a line, with a hole at x = −1.
f ( x) =
x +1 x +1 = 2 x − x − 6 ( x − 3)( x + 2)
Domain: all real numbers except x = 3, −2 Vertical asymptotes: x = 3, x = −2 Horizontal asymptote: y = 0