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

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

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

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

Problem 1

Problem 2

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.

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.

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}.

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}.

Problem 5 (Problem 6 in Book)

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