2.9. Vertical Asymptotes http://www.ck12.org
The holes are at(− 2 , 256 ),( 3 ,^1225 ).
Practice
- Write a function that fits the following criteria:
- Vertical asymptotes at 1 and 4
- Zeroes at 3 and 5
- Hole at (6, 3)
- Write a function that fits the following criteria:
- Vertical asymptotes at -2 and 2
- Zeroes at 1 and 5
- Hole at (3, -4)
- Write a function that fits the following criteria:
- Vertical asymptotes at 0 and 3
- Zeroes at 1 and 2
- Hole at (8, 21)
- Write a function that fits the following criteria:
- Vertical asymptotes at 2 and 6
- Zero at 5
- Hole at (4, 1)
- Write a function that fits the following criteria:
- Vertical asymptote at 4
- Zeroes at 0 and 3
- Hole at (5, 10)
Give the equations of the vertical asymptotes for the following functions.
6.f(x) =(x−(^22 −)(xx)− 4 )
7.g(x) =(x+ 1 −)(xx− 3 )
8.h(x) = 6 −(x+x 1 )(+^2 x− 5 )
9.j(x) =x^10 − 3 −(x+ 2 )(xx− 3 )
10.k(x) = 2 −(x+(^43 −)(xx)− 4 )
Identify the holes and equations of the vertical asymptotes of the following rational functions.
11.f(x) = 43 ((xx−+^14 )()( 2 x++x^1 )()(x 4 −−x^4 )()(xx++^41 ))
12.g(x) = 7 x((xx+− 13 )()( 1 x+−^8 x)()(x 3 −−x^3 )()(xx−+^48 ))
State the domain of the following rational functions.
13.h(x) =x(xx+( 31 )(−xx−)(x^3 −)(x 1 +)^4 )