1. Warm up: Get 2 color pencils and a ruler Give your best definition and one example of the following: Domain Range Ratio Leading coefficient

2. Chapter 9: “Let’s Be Rational About This” In this Unit you will learn to…  9.a: determine key characteristics of simple rational functions [9.1]  9.b: multiply and divide rational expressions [9.3]  9.c: add and subtract rational expressions [9.4]

3. 9.a: determine key characteristics of simple rational functions [9.1] After this lesson you will be able to…  Identify and graph a rational function.  Determine the domain and range of a rational function.  Determine the horizontal and vertical asymptotes of a rational function.  Determine how to find holes in rational functions.

4. What is a Rational Function? A rational function is the ratio of two polynomial expressions. In order for a function to be rational it must meet the following requirements: 1. f(x)= 2. p(x) and q(x) are polynomial functions. 3. q(x) 0 (The denominator cannot equal 0)

5. Is this function rational? Quick Definition: A Rational Function MUST have an ____________ in the __________________________________________.

6. Graph it

7. Vertical Asymptote  The red line is called a vertical asymptote. Vertical Asymptote: The vertical line the graph will not cross because that x value causes a zero in the denominator.

8. 1. Are there any values of x that make the function undefined (denom = 0)? 2. To find algebraically: a) Set the denominator = 0 b) Solve for x. 3. The line x= -1 is a vertical asymptote. Identify the Vertical Asymptote

9. Identify the Horizontal Asymptote  The blue line is a horizontal asymptote.  The horizontal line the graph will not cross because some x value causes a zero in the denominator.

10. Identify the Domain  Domain: All the x-values that DO work in the function. What can x equal? Are there any values that x cannot equal? For our function: D: __________________________

11. Identify the Range  Range: All the y-values that DO work for the function. What can y equal? Are there any values that y cannot equal? For our function: R: ____________________________

12. Try this one:  Graph the function  Find: Vertical Asymptote:_______________ Horizontal Asymptote:_____________ Domain:________________________ Range:_________________________

13. Try this one:  Graph the function  Find: Vertical Asymptote:_______________ Horizontal Asymptote:_____________ Domain:________________________ Range:_________________________

14. What did we learn?