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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) = x2 − 7x + 12x2 + 2x − 15
3.f(x) = x2 + x − 42x2 − 10x + 24
4.f(x) = x2 − 10x + 16x2 − 8x + 12
5.f(x) = x2 − 14x + 48x2 − x − 30
6.f(x) = x2 + 5x + 4x2 − 2x − 24
7.f(x) = x2 + 3x − 4x2 + 9x + 20
8.f(x) = x2 + 11x + 24x2 + 7x + 12
9.f(x) = x2 + 7x + 12x2 − 2x − 24
10.f(x) = x2 − 4x2 + 8x + 12
11.f(x) = x2 − 5x + 6x2 − 8x + 15
12.f(x) = x2 − 6x + 8x2 − x − 12
Answer key — Asymptotes and holes of rational functions practice
Asymptotes and holes of rational functions
1.vertical asymptote: x = −5; horizontal asymptote: y = 1; hole at (3, −18)
2.vertical asymptote: x = 1; horizontal asymptote: y = 1; hole at (0, −4)
3.vertical asymptote: x = 4; horizontal asymptote: y = 1; hole at (6, 132)
4.vertical asymptote: x = 6; horizontal asymptote: y = 1; hole at (2, 32)
5.vertical asymptote: x = −5; horizontal asymptote: y = 1; hole at (6, −211)
6.vertical asymptote: x = 6; horizontal asymptote: y = 1; hole at (−4, 310)
7.vertical asymptote: x = −5; horizontal asymptote: y = 1; hole at (−4, −5)
8.vertical asymptote: x = −4; horizontal asymptote: y = 1; hole at (−3, 5)
9.vertical asymptote: x = 6; horizontal asymptote: y = 1; hole at (−4, 110)
10.vertical asymptote: x = −6; horizontal asymptote: y = 1; hole at (−2, −1)
11.vertical asymptote: x = 5; horizontal asymptote: y = 1; hole at (3, −12)
12.vertical asymptote: x = −3; horizontal asymptote: y = 1; hole at (4, 27)
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