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Pre-Calculus Assignment Sheet Unit 2: Monster Functions; Piecewise Functions; Composition of Functions

September 9-23, 2013

Date Lesson AssignmentMondaySept. 9th

EXPLORING TRANSFORMATIONS Notes pages 1 and 2Monster Functions (Day 1)

Pages 3 and 4

TuesdaySept. 10th

EXPLORING TRANSFORMATIONS Monster Functions (Day 2) OPEN HOUSE 6:00 to 8:30 PM

Page 5

WednesdaySept. 11th

Graphing Piecewise Functions Notes Page 6 Page 6

ThursdaySept. 12th

Writing Piecewise Functions Notes page 6 Pages 6 and 7

FridaySept. 13th

Finish piecewise, Determining even/odd functions algebraicallyNotes page 7

Page 7 Study: Quizlet on Monday over piecewise

MondaySept. 16th

Quizlet over PiecewiseOperations on Functions and Notes page 8Restricting the Domain (Part 1)

pp. 89 – 90 #s: 1,3, 7-23 ODD, 43, 44, 59

TuesdaySept. 17th

Composition of Functions & Composition of Inverses Notes p. 8 pp. 89 – 90 #s: 31 – 41 ODD, 45, 46, 47, 49Study: Quiz tomorrow over Operations & Composition of Functions

WednesdaySept. 18th

Quiz on Operations and Composition of FunctionsFinding the inverses Notes page 9More practice with one-to-one

Worksheet page 9

ThursdaySept. 19th

Domain Restrictions (Part 2)Difference Quotient Notes page 10

Worksheet page 11

FridaySept. 20th

Assign monster projects Review/ wrap up for Test #2

Study: TEST on Monday!

MondaySept. 23rd Test #2 Print Unit 3 from

www.thsmsali.weebly.com

NOTES Sept. 9 EXPLORING TRANSFORMATIONS

Sketch graphs of the following transformations of f(x). Give the domain and range.

1) 2)

D: __________ R: __________ D: __________ R: __________ D: __________ R: __________

3) 4) 5)

D: __________ R: __________ D: __________ R: __________ D: __________ R: __________

Page 1

6) 7) 8)

D: D: D:

R: R: R:

9) 10) 11)

D: D: D:

R: R: R:

12) 13) 14)

D: D: D:

R: R: R:

Page 2

HOMEWORK Sept. 9 EXPLORING TRANSFORMATIONS

Sketch graphs of the following transformations of f(x). Give the domain and range.

1) 2)

D: D: D:

R: R: R:

3) 4) 5)

D: D: D:

R: R: R:

6) 7) 8)

D: D: D:

R: R: R:

Continued on page 4

Page 3

9) 10)

D: D: D:

R: R: R:

11) 12) 13)

D: D: D:

R: R: R:

14) 15) 16)

D: D: D:

R: R: R:

Page 4

EXPLORI NG TRANSFORMATIONS #3 Sketch graphs of the following transformations of f(x). Give the domain and range.

y f(x) 1) y f( x) 2) y f(x)

D: D: D:

R: R: R:

3) y f(x) 4) y f(x 1) 5) y f( x )

D: D: D:

R: R: R:

6) y f(x) 4 7) y 2f(2x) 8) 1y f(x 2) 32

D: D: D:

R: R: R:

Page 5

HOMEWORK Sept. 10 EXPLORING TRANSFORMATIONS #3

NOTES Sept. 11 Graphing Piecewise Functions

I Graph the following piecewise functions on a separate piece of graph paper.

1) 2)

3) 4)

5) Evaluate: Find

HOMEWORK Sept. 11 Graphing Piecewise Functions

Graph the following piecewise functions on a separate piece of graph paper.

1) 2) 3)

II Evaluate.

10) Find

NOTES Sept. 12 Writing Piecewise Equations

Ex 1: Ex 2: Ex. 3 Ex 4:

HOMEWORK Sept. 12 Writing Piecewise Equations

1) 2) 3) 4)

Continued on Page 7

Page 6

5) 6) 7)

8) 9)

NOTES Sept. 13 Determining if a function is even, odd or neither algebraically.

Definition: f(x) is even if: f(x) is odd if: for each x in the domain of f.

Determine if the given functions are even, odd or neither. even, odd or neither

1.) _________________________________ ________________

2.) _________________________________ ________________

3.) _________________________________ ________________

4) _________________________________ ________________

HOMEWORK Sept. 13 Determining if a function is even, odd or neither algebraically.

1.) _________________________________ ________________

2.) _________________________________ ________________

3.) _________________________________ ________________

4.) _________________________________ ________________

5.) _________________________________ ________________

6.) _________________________________ ________________

Page 7

NOTES Sept. 16 Function Operations from graphs

Given f(x) and g(x) ANSWER QUESTIONS 1 – 11.

1) 2) 3) 4) 5) 6)

7) 8) 9) 10) 11)

For each of the following, find: a. b. c. d.

12. 13.

14. 15.

16. 17.

NOTES Sept. 17 Composition of Functions

I. Let , , , . Determine the following.

1. 2. 3. 4. 5.

6. 7. 8. 9.

II. Let , , , , . Determine the following.

10. 11. 12.

13. 14. 15.

III. Use the graphs from yesterday (top of this page) to answer the following questions.16. 17. 18.

V. The following are composite functions. Find and so that .

19. 20.

VI. Determine if and are inverses by using composition of functions.

21. 22.

23. 24. NOTES Sept. 18 Inverse Functions

I. Graph the original function (restrict the domain if necessary). Then graph the inverse on the same graph in a different color.

Page 8

1) 2) 3)

4) 5) 6)

II. Find the inverse of each relation. State the domain and range. Is the inverse a function. State why or why not.

7) 8) 9)

10) 11) 12)

III. Determine whether f(x) and g(x) are inverse functions. Restrict the domain, if necessary and then state the domain and range of each function.

13) 14)

15) 16) IV.

IV For each graph do the followinga) Restrict the domain to . Sketch the original and the inverse on the same graph in different colors.b) Restrict the domain to . Sketch the original and the inverse on the same graph in different colors.

17) 18) 19) 20)

HOMEWORK Sept. 18 Inverses, Operations and Composition of Functions

I. Find the inverse of each algebraically. Graph the original function (restrict the domain if necessary). Then graph the inverse on the same graph in a different color

1) 2) 3) 4) 5)

6) 7) 8) 9) 10)

II. Given , , and find the following.

11) 12) 13) 14)

15) 16) 17) 18)

NOTES Sept. 19 Difference Quotient Worksheet

I. For the given function find the requested value.

Page 9

1) , find 2) , find 3) , find

II. For each given function, find .

4) 5)

III. For each given function, find .

6) 7)

IV. For each given function, find . Simplify your results.

8) 9) 10)

HOMEWORK Sept. 19 Difference Quotient Worksheet

I. For the given function find the requested value.

Page 10

1) , find 2) , find 3) , find

II. For each given function, find .

4) 5)

III. For each given function, find .

6) 7)

IV. For each given function, find . Simplify your results.

8) 9) 10.)

Page 11