College Algebra, 2013a

340 Rational Functions
16. f(x) = x2 − 2x +1
x 3 + x 2 − 2x
Domain: (−∞, −2) ∪ (−2, 0) ∪ (0, 1) ∪ (1, ∞)
f(x) = x − 1
x(x +2) ,x≠1
No x-intercepts
No y-intercepts
Vertical asymptotes: x = −2 andx =0
As x →−2 − ,f(x) →−∞
As x →−2 + ,f(x) →∞
As x → 0 − ,f(x) →∞
As x → 0 + ,f(x) →−∞
Hole in the graph at (1, 0)
Horizontal asymptote: y =0
As x →−∞,f(x) → 0 −
As x →∞,f(x) → 0 +
y
5
4
3
2
1
−5 −4 −3 −2 −1 1 2 3 4 5
−1
−2
−3
−4
−5
x
17. f(x) = 1
x − 2
Shift the graph of y = 1 x
to the right 2 units.
3
2
1
y
−1 1 2 3 4 5
−1
x
−2
−3
18. g(x) =1− 3 x
Vertically stretch the graph of y = 1 x
by a factor of 3.
Reflect the graph of y = 3 x
about the x-axis.
Shift the graph of y = − 3 x
up 1 unit.
y
7
6
5
4
3
2
1
−6−5−4−3−2−1
−1
1 2 3 4 5 6
−2
−3
−4
−5
x