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) = 6(x + 5)x2 + 2x − 24
2.f(x) = −4(x + 1)x2 + 2x − 3
3.f(x) = 5(x − 6)x2 + 9x + 20
4.f(x) = 3(x + 8)x2 − 5x + 4
5.f(x) = 9(x − 7)x2 − 9x + 20
6.f(x) = −(x − 4)x2 − x − 30
7.f(x) = 6(x + 3)x2 − 10x + 24
8.f(x) = 9(x − 8)x2 − 10x + 24
9.f(x) = −3(x − 2)x2 − 3x
10.f(x) = 2(x − 2)x2 − 3x − 10
11.f(x) = −9(x − 7)x2 − 5x + 6
12.f(x) = 8(x)x2 − 9x + 18
Answer key — Asymptotes and holes of rational functions practice
Asymptotes and holes of rational functions
1.vertical asymptote: x = −6, x = 4; horizontal asymptote: y = 0
2.vertical asymptote: x = −3, x = 1; horizontal asymptote: y = 0
3.vertical asymptote: x = −5, x = −4; horizontal asymptote: y = 0
4.vertical asymptote: x = 1, x = 4; horizontal asymptote: y = 0
5.vertical asymptote: x = 4, x = 5; horizontal asymptote: y = 0
6.vertical asymptote: x = −5, x = 6; horizontal asymptote: y = 0
7.vertical asymptote: x = 4, x = 6; horizontal asymptote: y = 0
8.vertical asymptote: x = 4, x = 6; horizontal asymptote: y = 0
9.vertical asymptote: x = 0, x = 3; horizontal asymptote: y = 0
10.vertical asymptote: x = −2, x = 5; horizontal asymptote: y = 0
11.vertical asymptote: x = 2, x = 3; horizontal asymptote: y = 0
12.vertical asymptote: x = 3, x = 6; horizontal asymptote: y = 0
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