Worksheet A: (Topic 1.8) Rational Functions and Zeros Name: Solutions
Directions: Find the zeros for the following rational functions.
y=
( x + 3)( x − 2 ) x2 ( x − 3)( x − 6 )
1. 2. y = 3. y =
( x − 1)( x + 5) ( x − 1)( x + 2 ) ( x − 6 )( x − 2 )
There is a hole at 𝑥 = 6
1. Zeros: x = −3, 2 2. Zeros: x = 0 3. Zeros: x = 3
x 2 − x − 20 x2 − 9 x3 − 4 x 2 − 32 x
4. h ( x ) = 5. f ( x ) = 6. g ( x ) =
x 2 + x − 20 x 2 − 2 x − 15 2 x2 + 7 x − 4
There is a hole at 𝑥 = −3
There is a hole at 𝑥 = −4
4. Zeros: x = −4, 5
5. Zeros: x = 3
6. Zeros: x = 0, 8
Directions: The graphs of several rational functions are given below. Use the graphs to solve the following inequalities.
Graph of f Graph of g Graph of h
7. f ( x ) 0 8. g ( x ) 0 9. h ( x ) 0
(−∞, −1) ∪ (0, ∞) (−1,1] (−∞, −2] ∪ (−1,0] ∪ (1, ∞)
Directions: Solve the following inequalities. Write your answers using interal notation.
x+2 x−3
10. 0 (−2,1) 11. 0 (−∞, −5) ∪ (3, ∞)
x −1 x+5
𝐖𝐨𝐫𝐤𝐬𝐡𝐞𝐞𝐭 𝐀: Topic 1.8 Rational Functions and End Behavior
Directions: Find the zeros for the following rational functions.
y=
( x + 3)( x − 2 ) x2 ( x − 3)( x − 6 )
1. 2. y = 3. y =
( x − 1)( x + 5) ( x − 1)( x + 2 ) ( x − 6 )( x − 2 )
There is a hole at 𝑥 = 6
1. Zeros: x = −3, 2 2. Zeros: x = 0 3. Zeros: x = 3
x 2 − x − 20 x2 − 9 x3 − 4 x 2 − 32 x
4. h ( x ) = 5. f ( x ) = 6. g ( x ) =
x 2 + x − 20 x 2 − 2 x − 15 2 x2 + 7 x − 4
There is a hole at 𝑥 = −3
There is a hole at 𝑥 = −4
4. Zeros: x = −4, 5
5. Zeros: x = 3
6. Zeros: x = 0, 8
Directions: The graphs of several rational functions are given below. Use the graphs to solve the following inequalities.
Graph of f Graph of g Graph of h
7. f ( x ) 0 8. g ( x ) 0 9. h ( x ) 0
(−∞, −1) ∪ (0, ∞) (−1,1] (−∞, −2] ∪ (−1,0] ∪ (1, ∞)
Directions: Solve the following inequalities. Write your answers using interal notation.
x+2 x−3
10. 0 (−2,1) 11. 0 (−∞, −5) ∪ (3, ∞)
x −1 x+5
𝐖𝐨𝐫𝐤𝐬𝐡𝐞𝐞𝐭 𝐀: Topic 1.8 Rational Functions and End Behavior
