Section 11.2 Day 1 Rational Functions Algebra 1

Upcoming Dates Friday, April 6th: Quiz 10.1-11.2 Review day Thursday, April 5th Monday, April 9th: Unit 6 Part 1 Retake Day 1 Go over the retake review guide. It MUST be completed ahead of time. Thursday, April 12th: Unit 6 Part 1 Retake Day 2 Go over the first attempt at the unit test. Unit 6 Part 1 Retake Day 3 Schedule an appointment with Miss Keyvan to retake the test

Note Quiz 10.2 Graph 𝑦=− 𝑥−2 +3 What is the domain of your graph? What is the range of your graph? Write the domain and range of the first example problem we completed in Section 10.2 Challenge Write an equation of a radical function that has a domain of 𝑥≥2 and a range of 𝑦≤3.

Learning Targets Identify and graph a horizontal asymptote Identify and graph a vertical asymptote Graph a rational function using a table Determine the domain and range of a rational function

Horizontal Asymptote A horizontal line that the graph of the function approaches but never touches 𝑦=______ How many horizontal asymptotes could you have?

Vertical Asymptote A vertical line that the graph of a function approaches but never touches 𝑥=_______

Rational Function General Equation: 𝑦= 𝑎 𝑥−𝑏 +𝑐 where 𝑎≠0 Horizontal Asymptote: 𝑦=𝑐 Vertical Asymptote: 𝑥=𝑏 Example: 𝑦= 1 𝑥−2 +1 Horizontal Asymptote: 𝑦=1 Vertical Asymptote: 𝑥=2

Graphing Rational Function Procedure Identify the asymptotes Graph your asymptotes Create a table with the middle value the vertical asymptote (VA) Choose 2 values above and below the VA Plot the points and create a rational function shape

Example 1 Graph 𝑦= 2 𝑥−5 +3 HA: 𝑦=3 VA: 𝑥=5 Domain: 𝑥≠5 Range: 𝑦≠3 X Y 4 1 5 --- 6 7 Graph 𝑦= 2 𝑥−5 +3 HA: 𝑦=3 VA: 𝑥=5 Domain: 𝑥≠5 Range: 𝑦≠3

Example 2 Graph 𝑦= 1 𝑥+1 HA: 𝑦=0 VA: 𝑥=−1 Domain: 𝑥≠−1 Range: 𝑦≠0 X Y -3 -1/2 -2 -1 --- 1 1/2 Graph 𝑦= 1 𝑥+1 HA: 𝑦=0 VA: 𝑥=−1 Domain: 𝑥≠−1 Range: 𝑦≠0

Example 3 Graph 𝑦= 6 𝑥 −4 HA: 𝑦=−4 VA: 𝑥=0 Domain: 𝑥≠0 Range: 𝑦≠−4 X Y -2 -7 -1 -10 --- 1 2 Graph 𝑦= 6 𝑥 −4 HA: 𝑦=−4 VA: 𝑥=0 Domain: 𝑥≠0 Range: 𝑦≠−4

Example 4 Graph 𝑦= 1 𝑥−3 −2 HA: 𝑦=−2 VA: 𝑥=3 Domain: 𝑥≠3 Range: 𝑦≠−2 X Y X Y 1 -2.5 2 -3 3 --- 4 -1 5 -1.5 Graph 𝑦= 1 𝑥−3 −2 HA: 𝑦=−2 VA: 𝑥=3 Domain: 𝑥≠3 Range: 𝑦≠−2