Date 2612 Objective SWBAT graph Rational Functions Bell

Date: 2/6/12 Objective: SWBAT graph Rational Functions Bell Ringer: Reading Across the Content (Vocabulary) Section 2. 7 and 2. 8 Turn in Take Home Test HW Requests: None Homework: In Class: 24 -30 evens pg 247 #23 -29, 45 -61 all 3’s Discussion of Venn Diagram Project Due Mon. , 2/13 Announcements: Quiz Friday

Date: 2/7/12 See Notes Included Objective: SWBAT analyze Rational Functions and solve rational equations in one variable Bell Ringer: pg 246 #29 Turn in last week’s homework for Grade Book. HW Requests: As you desire Homework: pg 254 #1, 4, 7, 12, 13, 16 -18, 24, 25 Graph them please, leave in your calculator Carry over pg 247 #23 -29, 45 -61 all 3’s In class: pg 254 #2, 5, 8, 11, 15, 17, 23, 26 Announcements: Quiz Friday Discussion of Venn Diagram Project Due Mon. , 2/13

Date: 2/8/12 Objective: SWBAT analyze Rational Functions and solve rational equations in one variable Bell Ringer: pg 254 #11 (pg 246 #29) HW Requests: pg 254 #1, 4, 7, 12, 13, 16 -18, 24, 25 Graph them please, leave in your calculator Carry over pg 247 #23 -29, 45 -61 all 3’s Homework: pg 247 #58, 62; pg 254 #23 -30 Pg 252 -254 Ex. 5 -7; Read Sect. 2. 9 EX. 1 In class: pg 254 #2, 5, 8, 11, 15, 17, 23, 26 Announcements: Quiz Friday Discussion of Venn Diagram Project Due Tues. , 2/14

Date: 2/9/12 Objective: SWBAT analyze Rational Functions and solve rational equations in one variable Bell Ringer: Go over p 254 #28, 29 (pg 246 #29) HW Requests: pg 247 #58, 62; pg 254 #23 -30 pg 254 #1, 4, 7, 12, 13, 16 -18, 24, 25 Carry over pg 247 #23 -29, 45 -61 all 3’s; Homework: Read pg 252 Ex. 5 -7 Work pg 255 #31, 33 In class: Quiz Review Read pg 252 Ex. 5 -7 Work pg 255 #31, 33 Announcements: Quiz Friday Discussion of Venn Diagram Project Due Tues. , 2/14

Date: 2/10/12 Objective: SWBAT analyze Rational Functions and solve rational equations in one variable Bell Ringer: Quiz 2. 7, 2. 8 (20 minutes) HW Requests: Homework: pg 255 # 32 -34 Announcements: Venn Diagram Project Due Tues. , 2/14

Example Solving by Clearing Fractions • Solving Rational Functions by Clearing Fractions Steps: (Show all work) 1. Determine and the restrictions due to the denominators. 2. Find the LCD 3. Multiply all terms by LCD to clear the denominators. 4. Solve the resulting equation 5. Check your solutions to make sure there are no extraneous solutions. 6. Be sure to note (write out) the extraneous solutions if there any. Slide 2 - 8

Pre. Calculus Handout Name: _____________ Date: ________ Per: ______ For Step 1: If n > m, to find the end behavior asymptote, divide the denominator into the numerator. The resulting quotient is the end behavior asymptote. There is no horizontal asymptote. The asymptote is the quotient expression from your division.

Example Solving by Clearing Fractions Slide 2 - 10

Example Eliminating Extraneous Solutions Slide 2 - 11

Extraneous Solutions When we multiply or divide an equation by an expression containing variables, the resulting equation may have solutions that are not solutions of the original equation. These are extraneous solutions. For this reason we must check each solution of the resulting equation in the original equation. Slide 2 - 12

Step 1: If n > m, to find the end behavior asymptote, divide the denominator into the numerator. The resulting quotient is the end behavior asymptote. Slide 2 - 13

Example Finding Asymptotes of Rational Functions Slide 2 - 14

Example Graphing a Rational Function Slide 2 - 15