Pre-Calculus Assignment Sheet



Pre-Calculus Assignment Sheet

Unit 2 – Exploring Functions

September 10 – 25, 2012

|Date |Lesson |Assignment |

|Mon |Monster Functions (Day 1) |Worksheets p. 3 – 4 |

|Sept. 10 |EXPLORING TRANSFORMATIONS Notes p. 1 – 2 | |

|Tues |Monster Functions (Day 2) |Worksheet p. 5 |

|Sept. 11 |EXPLORING TRANSFORMATIONS |This will be collected tomorrow (Wed) |

|Wed |Graphing Piecewise Functions |Worksheet p. 6 (top) |

|Sept. 12 | |Study for Quiz |

|Thur |Writing Piecewise Functions Notes p. 6 |Worksheet p. 6 – 7 |

|Sept. 13 |Quiz – Monster Functions | |

|Fri |Piecewise Functions (cont’d) |Worksheet p. 7 |

|Sept. 14 |Determining even/odd functions algebraically Notes p. 7 |Begin Monster Project (due Mon, Sept 24) |

|Mon |Operations on Functions Notes p. 8 (top) |Textbook pp. 89 – 90 |

|Sept. 17 |Restricting the Domain (Part 1) |#1,3, 7-23 (odd), 43, 44, 59 |

|Tues |Composition of Functions Inverses Notes p. 8 (bottom) |FINISH Notes p. 8 |

|Sept. 18 |Quiz – Piecewise Functions |pp. 89 – 90 #s: 31 – 41 ODD, 45, 46, 47, 49 |

|Wed |Finding Inverses Notes p. 9 |Worksheet p. 9 |

|Sept. 19 |Domain Restrictions (Part 2) | |

|Thur |Finding Inverses (cont’d) |Worksheet p. 9 |

|Sept. 20 | |Study for Quiz |

|Fri |Difference Quotient Notes p. 10 |Worksheet p. 10 |

|Sept. 21 |Quiz – Operations and Composition of Functions |Complete Monster Project (due Mon) |

|Mon |Review/ wrap up for Test #2 |Study for Test |

|Sept. 24 |Monster Project DUE TODAY | |

|Tues |Test Unit 2 – Exploring Functions |Print Unit 3 from THS Website or at |

|Sept. 25 | |thsprecalculus. |

NOTES Sept. 10, 2012 EXPLORING TRANSFORMATIONS

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

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

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

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

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

[pic]

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

[pic] [pic] [pic]

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

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

[pic] [pic] [pic]

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

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

[pic] [pic] [pic]

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

HOMEWORK Sept. 10, 2012 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:

HOMEWORK Sept. 11 2012 TURN IN: Sept. 12th Name: _________________________ Per: ______

[pic]

HOMEWORK Sept. 12th , 2012 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) [pic] 6) [pic]

7) [pic] 8) [pic]

II Evaluate.

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

Find [pic] Find [pic] Find [pic]

NOTES Sept. 13th , 2012 Writing Piecewise Equations

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

HOMEWORK Sept. 13th , 2012 For each graph below, write a piecewise function. Put answers on separate paper!!!!!

1) 2) 3) 4)

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

continued on page 7 (

5) 6) 7) 8)

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

9) 10) 11) 12)

NOTES Sept. 14th, 2012 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. 14th, 2012

1.) [pic] [pic]_________________________________ ________________

2.) [pic] [pic]_________________________________ ________________

3.) [pic] [pic]_________________________________ ________________

4.) [pic] [pic]_________________________________ ________________

5.) [pic] [pic]_________________________________ ________________

6.) [pic] [pic]_________________________________ ________________

NOTES Sept. 17th, 2012 Operations on Functions – add, subtract, multiply, divide

Given the graphs of 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 pairs of functions, 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 18th, 2012 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. 19th- 20th, 2012 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. 19th – 20th, 2012 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. 21st, 2012 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]

H0MEWORK Sept. 21st, 2012 Difference Quotient Worksheet

I. For the given function find the requested value. Use separate paper or back of sheet 9.

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]

-----------------------

p.1

p.2

p.3

p.4

p.5

p.6

p.7

p.8

p.9

p.10

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