College Algebra, 2013a

336 Rational Functions
1
4. f(x) =
x 2 + x − 12 = 1
(x − 3)(x +4)
Domain: (−∞, −4) ∪ (−4, 3) ∪ (3, ∞)
No x-intercepts
y-intercept: (0, − 1
12 )
Vertical asymptotes: x = −4 andx =3
As x →−4 − ,f(x) →∞
As x →−4 + ,f(x) →−∞
As x → 3 − ,f(x) →−∞
As x → 3 + ,f(x) →∞
Horizontal asymptote: y =0
As x →−∞,f(x) → 0 +
As x →∞,f(x) → 0 +
y
1
−6 −5 −4 −3 −2 −1 1 2 3 4
−1
x
2x − 1
5. f(x) =
−2x 2 − 5x +3 = − 2x − 1
(2x − 1)(x +3)
Domain: (−∞, −3) ∪ (−3, 1 2 ) ∪ ( 1 2 , ∞)
No x-intercepts
y-intercept: (0, − 1 3 )
f(x) =
−1
x +3 ,x≠ 1 2
Hole in the graph at ( 1 2 , − 2 7 )
Vertical asymptote: x = −3
As x →−3 − ,f(x) →∞
As x →−3 + ,f(x) →−∞
Horizontal asymptote: y =0
As x →−∞,f(x) → 0 +
As x →∞,f(x) → 0 −
y
1
−7 −6 −5 −4 −3 −2 −1 1 2
−1
x
x
6. f(x) =
x 2 + x − 12 = x
(x − 3)(x +4)
Domain: (−∞, −4) ∪ (−4, 3) ∪ (3, ∞)
x-intercept: (0, 0)
y-intercept: (0, 0)
Vertical asymptotes: x = −4 andx =3
As x →−4 − ,f(x) →−∞
As x →−4 + ,f(x) →∞
As x → 3 − ,f(x) →−∞
As x → 3 + ,f(x) →∞
Horizontal asymptote: y =0
As x →−∞,f(x) → 0 −
As x →∞,f(x) → 0 +
y
1
−6 −5 −4 −3 −2 −1 1 2 3 4 5
−1
x