Date: 10/17/11- Section: 1.3Obj.: SWBAT analyze the behaviors of 12 Basic Functions by finding the domain, range, continuity, increasingness, decreasingness, symmetry, bounding, and local extrema.Bell Ringer: Solve using the quadratic formula: x2 – 4x – 8 = 0.Get a White Board and marker

Homework Requests: Turn In pg 109 #1-18

In class: Graphing the 12 Basic Functions. Worksheet: Matching the Graph of a Function with its Equation (Exit Ticket)

Homework: pg 109 #19-24, 27, 28.

Announcements: No calculator sharing on tests.Turn in missing assignments Grades due next week.Quiz Friday

Domain (look at x values): Starts with D= (-∞, ∞)Restrictions?1. Square Root? No Yes -> arg ≥ 0

Ex: 9-t≥ 0 t≤9

D= (-∞, ∞) D= (-∞, 9]2. Denominator? No Yes -> Denominator cannot = 0 Denom. ≠ 0

Ex 1: Find what makes denom. =0 -> 9-t= 0 -> t= 9 D= (-∞, ∞) Domain already restricted to D= (-∞, 9] due to square root

t ≠ 9; D= (-∞, 9) Ex 2: Find what makes denom. =0 2x+4 = 0 x=-2

x cannot = -2 x≠ -2 D= (-∞,-2) U (-2, ∞)

Range look at your y values. 1. Square Root and Absolute value (y values ≥ 0) R = [0, ∞)

Bell Ringer: Solve using the quadratic formula: x2 – 4x – 8 = 0.

Domain/Range Review

Date: 10/18/11- Section: 1.3Objective: SWBAT find horizontal and vertical asymptotes and end behavior using algebraic properties and graphical methods.Bell Ringer: Simplify the following: a. (2x6)7, b. , c. 13x3 · 12x4, d. 5 minutes to complete Handout Match Functions.

Homework Requests: pg 109 #19-24, 27, 28.. In Class: (pg 99 #63-66), Exit Ticket: pg 99, #59, 60, 61, 65, 110 #25 , 26Homework: pg 110 #35-44,

Announcements: No calculator sharing on tests.Turn in missing assignments w/reinstatement 2 missing assignments accepted turn in by Friday 10/2110 week Exam 10/26 Wed.Grades due next week.Quiz Friday

Horizontal AsymptotesWhat happens to the function when x gets very large (positive or negative)? If y = b, then this is the horizontal asymptote.

Vertical AsymptotesWhat happens when the function blows up? The function goes to +/-∞ at a point a.

Bell Ringer: Simplify the following: a. (2x6)7, b. , c. 13x3 · 12x4, d.

Asymptote Tests:Horizontal Asymptotes (Case +∞, Case - ∞)Examine the Function: 1. Algebraic solution: y= As x gets large this function begins to behave like y= or y= Case +∞ positive x gets large this fraction approaches ½ Case -∞ negative x gets large this fraction approaches ½2. Numerical solution y= . Case +∞ For x substitute in a very large positive value like 1000000000. Then look at the value of y. Case - ∞ Substitute in a very large negative value like -10000000000. Then look at the value of y. Both cases: If y “hangs” around a value y=b, then this is the horizontal asymptote. Be very careful with parentheses.3. Table: Look at table for large + and - values of x. If y “hangs” around a value y=b, then this is the horizontal asymptote.

Vertical AsymptotesLook for places where the function blows up. The denominator ≠ 0. The vertical asymptote is where the function goes to +/- infinity.y= . Find where denom. = 0 Solve 2x+1 = 0 denom. ≠ 0 x ≠ -1/2 vert. asymptote = - ½

End Behavior – Test like the horizontal asymptote test

Bell Ringer: Simplify the following: a. (2x6)7, b. , c. 13x3 · 12x4, d. In Class: (pg 99 #63-66),

Date: 10/19/11- Section: 1.3Objective: SWBAT find horizontal and vertical asymptotes and end behavior using algebraic properties and graphical methods.Bell Ringer: Go over the 1.2 Test

Homework Requests: Questions about the Matching graphs worksheet.

In Class: (pg 99 #63-66), Exit Ticket: pg 99, #59, 60, 61, Homework pg 110 #35-44, Worksheet 12 Basic Functions due Friday.Announcements: No calculator sharing on tests.Turn in missing assignments w/reinstatement 2 missing assignments accepted turn in by Friday 10/2110 week Exam 10/26 Wed.Grades due next week.Quiz Friday

Date: 10/20/11- Section: 1.3Objective: SWBAT find horizontal and vertical asymptotes and end behavior using algebraic properties and graphical methods.Bell Ringer: Go over the 1.2 Test

Homework Requests: pg 110 #35-44,

In Class: (pg 99 #63-66), Exit Ticket: pg 99, #59, 60, 61, Homework:Worksheet 12 Basic Functions due Friday. Pg 110 #46-52 evensAnnouncements: No calculator sharing on tests.Turn in missing assignments w/reinstatement 2 missing assignments accepted turn in by Friday 10/2110 week Exam 10/26 Wed.Grades due next week.Quiz Friday

Date: 10/21/11- Section: 1.4Objective: Combining functions algebraicallyBell Ringer: Quiz Section 1.3 (10 minutes)

Homework Requests: Go over worksheet for end behavior (5 minutes)

In Class: Talk about piece wise functions (10 minutes)Group work: See board Homework: pg 110 #48, 50; pg 127 #1-6

Announcements: No calculator sharing on tests.Turn in missing assignments w/reinstatement 2 missing assignments accepted turn in by Friday 10/2110 week Exam 10/26 Wed.Grades due next week.Quiz Friday

Slide 1- 9

Sum, Difference, Product, and Quotient

Let and be two functions with intersecting domains. Then for all values of in the intersection, the algebraic combinations of and are defined by the following rules:Sum: ( ) ( )

Differ

f gx f g

f g x f x g x

ence: ( ) ( ) ( )

Product: ( )( ) ( ) ( )

( )Quotient: , provided ( ) 0( )

In each case, the domain of the new function consists of all numbers that belong to both the domain of and

f g x f x g x

fg x f x g x

f f xx g xg g x

f

the domain of . g