Name ______________________Date ____________Score ____ / 12
Asymptotes and holes of rational functions practice
Asymptotes and holes of rational functions · 1–12
Find the vertical and horizontal asymptotes, and any hole.
1.f(x) = −3(x − 6)x2 − 2x − 3
2.f(x) = −9(x + 3)x2 − 2x − 24
3.f(x) = −4(x − 2)x2 − 2x − 8
4.f(x) = 6(x − 5)x2 − 2x − 8
5.f(x) = 3(x + 5)x2 + 7x + 6
6.f(x) = 5(x + 1)x2 − 6x + 5
7.f(x) = 2(x − 2)x2 − 5x − 6
8.f(x) = (x − 7)x2 − 2x − 8
9.f(x) = 2(x + 8)x2 + 7x + 6
10.f(x) = 3(x + 7)x2 − 7x + 12
11.f(x) = −8(x − 8)x2 − x − 6
12.f(x) = −(x − 1)x2 − 36
Answer key — Asymptotes and holes of rational functions practice
Asymptotes and holes of rational functions
1.vertical asymptote: x = −1, x = 3; horizontal asymptote: y = 0
2.vertical asymptote: x = −4, x = 6; horizontal asymptote: y = 0
3.vertical asymptote: x = −2, x = 4; horizontal asymptote: y = 0
4.vertical asymptote: x = −2, x = 4; horizontal asymptote: y = 0
5.vertical asymptote: x = −6, x = −1; horizontal asymptote: y = 0
6.vertical asymptote: x = 1, x = 5; horizontal asymptote: y = 0
7.vertical asymptote: x = −1, x = 6; horizontal asymptote: y = 0
8.vertical asymptote: x = −2, x = 4; horizontal asymptote: y = 0
9.vertical asymptote: x = −6, x = −1; horizontal asymptote: y = 0
10.vertical asymptote: x = 3, x = 4; horizontal asymptote: y = 0
11.vertical asymptote: x = −2, x = 3; horizontal asymptote: y = 0
12.vertical asymptote: x = −6, x = 6; horizontal asymptote: y = 0
mathsheetstudio.commathsheetstudio.commathsheetstudio.commathsheetstudio.commathsheetstudio.commathsheetstudio.commathsheetstudio.commathsheetstudio.com