1. Attributes and Transformations of Reciprocal Functions
Unit 9: Rational Functions
Lesson 11-2 in Textbook (pg. 457)

2. Essential Question
How are reciprocal functions different than other types of functions we have studied this year?

3. Vocabulary
Rational Function: 𝑓 𝑥 = 𝑃(𝑥) 𝑄(𝑥) , where 𝑃(𝑥) and 𝑄(𝑥) are polynomial functions.
Remember: “rational” basically means “fraction”

4. Vocabulary (cont)
A reciprocal function belongs to the family whose parent function is 𝑓 𝑥 = 1 𝑥 where 𝑥≠0.

6. Problem 1

9. Problem 2

11. Problem 3
To obtain the graph of 𝑦= 1 𝑥 +2, you can shift the graph of 𝑦= 1 𝑥 up 2 units.
Notice that this will also shift the horizontal asymptote up 2 units to 𝑦=2,
and change the range of the function to the set of y-values such that 𝑦>2 or 𝑦<2.
The domain will not change, so the domain is the set of x-values such that 𝑥>0 or 𝑥<0.

12. Problem 3
To obtain the graph of 𝑦= 1 𝑥 −3, you can shift the graph of 𝑦= 1 𝑥 down 3 units.
Notice that this will also shift the horizontal asymptote down 3 units to 𝑦=−3,
and change the range of the function to the set of y-values such that 𝑦>−3 or 𝑦<−3.
The domain is the set of x-values such that 𝑥>0 or 𝑥<0.

13. Problem 4
To obtain the graph of 𝑦= 1 𝑥−1 , you can shift the graph of 𝑦= 1 𝑥 right 1 unit.
Notice that this will also shift the vertical asymptote right 1 unit to 𝑥=1,
and change the domain of the function to {𝑥|𝑥≠1}.
The range of the function will not change, and is {𝑦|𝑦≠0}.

14. Problem 4
To obtain the graph of 𝑦= 1 𝑥+2 , you can shift the graph of 𝑦= 1 𝑥 left 2 units.
Notice that this will also shift the vertical asymptote left 2 units to 𝑥=−2.
The domain of the function is {𝑥|𝑥≠−2}.
The range is {𝑦|𝑦≠0}.

15. Problem 5 (Problem 6 in Book)

17. Complete 1-8 on the worksheet.
Assignment
Complete 1-8 on the worksheet.