Pre-Calculus Assignment Sheet



Pre-Calculus Assignment Sheet

Unit 2: Monster Functions; Piecewise Functions; Composition of Functions

September 9-23, 2013

|Date |Lesson |Assignment |

|Monday |EXPLORING TRANSFORMATIONS Notes pages 1 and 2 |Pages 3 and 4 |

|Sept. 9th |Monster Functions (Day 1) | |

|Tuesday |EXPLORING TRANSFORMATIONS |Page 5 |

|Sept. 10th |Monster Functions (Day 2) | |

| | | |

| |OPEN HOUSE 6:00 to 8:30 PM | |

|Wednesday |Graphing Piecewise Functions Notes Page 6 |Page 6 |

|Sept. 11th | | |

|Thursday |Writing Piecewise Functions Notes page 6 |Pages 6 and 7 |

|Sept. 12th | | |

|Friday |Finish piecewise, Determining even/odd functions algebraically |Page 7 |

|Sept. 13th |Notes page 7 |Study: Quizlet on Monday over piecewise |

|Monday |Quizlet over Piecewise |pp. 89 – 90 #s: 1,3, 7-23 ODD, 43, 44, 59 |

|Sept. 16th |Operations on Functions and Notes page 8 | |

| |Restricting the Domain (Part 1) | |

|Tuesday |Composition of Functions & Composition of Inverses Notes p. 8 |pp. 89 – 90 #s: 31 – 41 ODD, 45, 46, 47, 49 |

|Sept. 17th | |Study: Quiz tomorrow over Operations & |

| | |Composition of Functions |

|Wednesday |Quiz on Operations and Composition of Functions |Worksheet page 9 |

|Sept. 18th |Finding the inverses Notes page 9 | |

| |More practice with one-to-one | |

|Thursday |Domain Restrictions (Part 2) |Worksheet page 11 |

|Sept. 19th |Difference Quotient Notes page 10 | |

|Friday |Assign monster projects |Study: TEST on Monday! |

|Sept. 20th |Review/ wrap up for Test #2 | |

|Monday |Test #2 |Print Unit 3 from thsmsali. |

|Sept. 23rd | | |

NOTES Sept. 9 EXPLORING TRANSFORMATIONS

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

[pic] 1) [pic] 2) [pic]

[pic] [pic] [pic]

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

3) [pic] 4) [pic] 5) [pic]

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

6) [pic] 7) [pic] 8) [pic]

[pic] [pic] [pic]

D: D: D:

R: R: R:

9) [pic] 10) [pic] 11) [pic]

[pic] [pic] [pic]

D: D: D:

R: R: R:

12) [pic] 13) [pic] 14) [pic]

[pic] [pic] [pic]

D: D: D:

R: R: R:

HOMEWORK Sept. 9 EXPLORING TRANSFORMATIONS

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

[pic] 1) [pic] 2) [pic]

[pic] [pic] [pic]

D: D: D:

R: R: R:

3) [pic] 4) [pic] 5) [pic]

[pic] [pic] [pic]

D: D: D:

R: R: R:

6) [pic] 7) [pic] 8) [pic]

[pic] [pic] [pic]

D: D: D:

R: R: R:

Continued on page 4

[pic] 9) [pic] 10) [pic]

[pic]

D: D: D:

R: R: R:

11) [pic] 12) [pic] 13) [pic]

[pic] [pic] [pic]

D: D: D:

R: R: R:

14) [pic] 15) [pic] 16) [pic]

[pic] [pic] [pic]

D: D: D:

R: R: R:

[pic]

NOTES Sept. 11 Graphing Piecewise Functions

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

1) [pic] 2) [pic]

3) [pic] 4) [pic]

5) Evaluate: [pic] ( Find [pic]

HOMEWORK Sept. 11 Graphing Piecewise Functions

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

1) [pic] 2) [pic] 3) [pic]

II Evaluate.

10) [pic] ( Find [pic]

NOTES Sept. 12 Writing Piecewise Equations

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

HOMEWORK Sept. 12 Writing Piecewise Equations

1) 2) 3) 4)

[pic] [pic][pic][pic]

Continued on Page 7

5) 6) 7)

[pic] [pic] [pic]

8) 9)

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

Definition: f(x) is even if: [pic]

f(x) is odd if: [pic] for each x in the domain of f.

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

1.) [pic] [pic]_________________________________ ________________

2.) [pic] [pic]_________________________________ ________________

3.) [pic] [pic]_________________________________ ________________

4) [pic] [pic]_________________________________ ________________

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

1.) [pic] [pic]_________________________________ ________________

2.) [pic] [pic]_________________________________ ________________

3.) [pic] [pic]_________________________________ ________________

4.) [pic] [pic]_________________________________ ________________

5.) [pic] [pic]_________________________________ ________________

6.) [pic] [pic]_________________________________ ________________

NOTES Sept. 16 Function Operations from graphs

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

1) [pic] 2) [pic] 3) [pic] 4) [pic] 5) [pic] 6) [pic]

7) [pic] 8) [pic] 9) [pic] 10) [pic] 11) [pic]

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

12. [pic] [pic] 13. [pic] [pic]

14. [pic] [pic] 15. [pic] [pic]

16. [pic] [pic] 17. [pic] [pic]

NOTES Sept. 17 Composition of Functions

I. Let [pic], [pic], [pic], [pic]. Determine the following.

1. [pic] 2. [pic] 3. [pic] 4. [pic] 5. [pic]

6. [pic] 7. [pic] 8. [pic] 9. [pic]

II. Let [pic], [pic], [pic], [pic], [pic]. Determine the following.

10. [pic] 11. [pic] 12. [pic]

13. [pic] 14. [pic] 15. [pic]

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

16. [pic] 17. [pic][pic] 18. [pic]

V. The following are composite functions. Find [pic] and [pic] so that [pic].

19. [pic] 20. [pic]

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

21. [pic] [pic] 22. [pic] [pic]

23. [pic] [pic] 24. [pic] [pic]

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.

1) [pic] 2) [pic] 3) [pic]

4) [pic] 5) [pic] 6) [pic]

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

7) [pic] 8) [pic] 9) [pic]

10) [pic] 11) [pic] 12) [pic]

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) [pic] [pic] 14) [pic] [pic]

15) [pic] [pic] 16) [pic] [pic]IV.

IV For each graph do the following

a) Restrict the domain to [pic]. Sketch the original and the inverse on the same graph in different colors.

b) Restrict the domain to [pic]. Sketch the original and the inverse on the same graph in different colors.

17) 18) 19) 20)

[pic] [pic] [pic] [pic]

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) [pic] 2) [pic] 3) [pic] 4) [pic] 5) [pic]

6) [pic] 7) [pic] 8) [pic] 9) [pic] 10) [pic]

II. Given [pic], [pic], and [pic] find the following.

11) [pic] 12) [pic] 13) [pic] 14) [pic]

15) [pic] 16) [pic] 17) [pic] 18) [pic]

NOTES Sept. 19 Difference Quotient Worksheet

I. For the given function find the requested value.

1) [pic], find [pic] 2) [pic], find [pic] 3) [pic], find [pic]

II. For each given function, find [pic].

4) [pic] 5) [pic]

III. For each given function, find [pic].

6) [pic] 7) [pic]

IV. For each given function, find [pic]. Simplify your results.

8) [pic] 9) [pic] 10) [pic]

HOMEWORK Sept. 19 Difference Quotient Worksheet

I. For the given function find the requested value.

1) [pic], find [pic] 2) [pic], find [pic] 3) [pic], find [pic]

II. For each given function, find [pic].

4) [pic] 5) [pic]

III. For each given function, find [pic].

6) [pic] 7) [pic]

IV. For each given function, find [pic]. Simplify your results.

8) [pic] 9) [pic] 10.) [pic]

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HOMEWORK Sept. 10 EXPLORING TRANSFORMATIONS #3

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