Pre-Calculus Assignment Sheet
Unit 2 – Exploring Functions
September 10 – 25, 2012
Date
Mon
Sept. 10
Tues
Sept. 11
Wed
Sept. 12
Thur
Sept. 13
Fri
Sept. 14
Mon
Sept. 17
Tues
Sept. 18
Wed
Sept. 19
Thur
Sept. 20
Fri
Sept. 21
Mon
Sept. 24
Tues
Sept. 25
Lesson
Monster Functions (Day 1)
EXPLORING TRANSFORMATIONS Notes p. 1 – 2
Monster Functions (Day 2)
EXPLORING TRANSFORMATIONS
Graphing Piecewise Functions
Writing Piecewise Functions Notes p. 6
Quiz – Monster Functions
Piecewise Functions (cont’d)
Determining even/odd functions algebraically Notes p. 7
Operations on Functions Notes p. 8 (top)
Restricting the Domain (Part 1)
Composition of Functions Inverses Notes p. 8 (bottom)
Quiz – Piecewise Functions
Finding Inverses Notes p. 9
Domain Restrictions (Part 2)
Finding Inverses (cont’d)
Difference Quotient
Notes p. 10
Quiz – Operations and Composition of Functions
Review/ wrap up for Test #2
Monster Project DUE TODAY
Test Unit 2 – Exploring Functions
Assignment
Worksheets p. 3 – 4
Worksheet p. 5
This will be collected tomorrow (Wed)
Worksheet p. 6 (top)
Study for Quiz
Worksheet p. 6 – 7
Worksheet p. 7
Begin Monster Project (due Mon, Sept 24)
Textbook pp. 89 – 90
#1,3, 7-23 (odd), 43, 44, 59
FINISH Notes p. 8
pp. 89 – 90 #s: 31 – 41 ODD, 45, 46, 47, 49
Worksheet p. 9
Worksheet p. 9
Study for Quiz
Worksheet p. 10
Complete Monster Project (due Mon)
Study for Test
Print Unit 3 from THS Website or at
www.thsprecalculus.weebly.com
NOTES Sept. 10, 2012
EXPLORING TRANSFORMATIONS
Sketch graphs of the following transformations of f(x). Give the domain and range.
y  f(x)
1) y  f(x  2)
D: __________ R: __________
D: __________ R: __________
3) y  f(x)  2
4) y  f(x)  2
D: __________ R: __________
D: __________ R: __________
2) y  f(x  2)
D: __________ R: __________
5) y  2f(x)
D: __________ R: __________
p.1
y  f(x)
6) y 
1
2
f(x)
7) y  f
 
1
2
x
8) y  f(2x)
D: __________ R: __________
D: __________ R: __________
D: __________ R: __________
9) y  f(  x)
10) y   f(x)
11) y 
D: __________ R: __________
D: __________ R: __________
D: __________ R: __________
12) y  f  x 
13) y 
D: __________ R: __________
D: __________ R: __________
1
2
f(2x)
14) y 
f(x)
f x
D: __________ R: __________
p.2
HOMEWORK
Sept. 10, 2012
EXPLORING TRANSFORMATIONS
Sketch graphs of the following transformations of f(x). Give the domain and range.
1) y   f(x)
2) y  f(  x)
D:
D:
D:
R:
R:
R:
4) y  f( x )
5) y 
D:
D:
D:
R:
R:
R:
6) y  2f  x 
7) y 
D:
D:
D:
R:
R:
R:
y  f(x)
3) y 
f(x)
1
2
f(x)
1
2
f(2x)
8) y  f(x  1)  2
continued on page 4 
p.3
9) y  f(  x)
10) y 
D:
D:
D:
R:
R:
R:
11) y   f(x)
12) y  f(x  1)
13) y  f( x )
D:
D:
D:
R:
R:
R:
14) y  f(x)  4
15) y  2f(2x)
16) y 
D:
D:
D:
R:
R:
R:
y  f(x)
f(x)
1
2
f(x  2)  3
p.4
HOMEWORK Sept. 11 2012
TURN IN: Sept. 12th
Name: _________________________ Per: ______
EXPLORING TRANSFORMATIONS #3
Sketch graphs of the following transformations of f(x). Give the domain and range.
y  f(x)
1)
y  f(  x)
2)
D:
D:
D:
R:
R:
R:
3)
y   f(x)
4)
y  f(x  1)
5)
D:
D:
D:
R:
R:
R:
6)
y  f(x)  4
7)
y  2f(2x)
8)
D:
D:
D:
R:
R:
R:
y 
f(x)
y  f( x )
y 
1
2
f(x  2)  3
p.5
Sept. 12th , 2012
HOMEWORK
Graphing Piecewise Functions
I Graph the following piecewise functions on a separate piece of graph paper.
2 x  3 if x  1
3) f ( x)  
 x  1 if 1  x  6
 x 2  2 if x  1
1) f ( x)  
3x  5 if 1  x  3
 x2
2) f ( x)  
x 1
5  x if x  2
4) f ( x)  
 x  1 if 2  x  5
3x  4 if 0  x  3
5) f ( x)  
1  x if  3  x  0
3  x, x  1
9) f(x)  
2x, x  1
Find f(0), f(1), f(2.5)
NOTES
Ex 1:
HOMEWORK
1)
if x  0
1
 , x0
10) f(x)   x
x, x  0
11)

1, x  0
f(x)  

 x, x  0
Find f(1), f(0), f(5)
Find f(1), f(0), f( )
Sept. 13th , 2012
3 if x  2
6) f ( x)  
4 if x  2

 x2
if x  0

if 0  x  2
8) f ( x)   x  3
1
 x  1 if x  2
2
2 x  3 if x  1

7) f ( x)   x  5 if  1  x  2
 2
if x  2
x
II Evaluate.
if x  0
Writing Piecewise Equations
Ex 2:
Sept. 13th , 2012
2)
Ex. 3
Ex 4:
For each graph below, write a piecewise function. Put answers on separate paper!!!!!
3)
4)
continued on page 7 
p.6
5)
6)
7)
8)
9)
10)
11)
12)
NOTES
Sept. 14th, 2012
Definition:
f(x) is even if:
f(x) is odd if:
Determining if a function is even, odd or neither algebraically.
f ( x)  f ( x)
f ( x)   f ( x)
for each x in the domain of f.
Determine if the given functions are even, odd or neither.
even, odd or neither
1.)
f ( x)  x 6  2 x 2  3
f ( x)  _________________________________
________________
2.)
f ( x)  x 3  3 x
f ( x)  _________________________________
________________
3.)
f ( x)  7 x 2  x  1
f ( x)  _________________________________
________________
4)
f ( x)  x 5
f ( x)  _________________________________
________________
4
Sept. 14th, 2012
HOMEWORK
1.)
f ( x)  2 x 7  3 x 5  5 x
f ( x)  _________________________________
________________
2.)
f ( x)  x x 2  1
f ( x)  _________________________________
________________
3.)
f ( x)  3 x 5  2 x 2  4
f ( x)  _________________________________
________________
f ( x)  _________________________________
________________
2
3
4.)
f ( x)  4 x
5.)
f ( x)  3x 8  7 x 5  4 x  10
f ( x)  _________________________________
________________
6.)
f ( x)  12 x 6  8x 4  3x 2  1
f ( x)  _________________________________
________________
p.7
Sept. 17th, 2012
NOTES
Operations on Functions – add, subtract, multiply, divide
Given the graphs of f(x) and g(x) ANSWER QUESTIONS 1 – 11.
1)
1
g(9)
3
2) ( g  f )(10)
7) ( f  g )( 6)
8) 2 f ( 9)
3) ( fg )( 6)
g
(1)
f
9) 
10)
14.)
f (x)  x 2  4
16.) f ( x )  2 x  1
g(x)  x  2
b. ( f  g)(x)
d. 
g ( x)  2 x
g(x)  x 3
g ( x)  x 2  3 x  2
Sept 18th, 2012 Composition of Functions
NOTES
h( x)  2 x 2  3 ,
j ( x )  3 x .
I. Let f ( x)  x  5 ,
g ( x)  3x  1 ,
1. f ( g ( x))
2. g ( f ( x))
3. ( f  h)( 2)
4. (h  j )(16)
6. j ( f ( x ))
7. f ( f (3))
8. g (h( j (2)))
9. ( f  j  h)( x )
II. Let
 f
(x)
 g 
c. ( fg)(x)
f ( x)  3x 2  4
x
15.) f (x) 
x 1
2
17.) f ( x)  x
g ( x)  x 2  3
6) 
11) at x  3, f ( x )  4
13.)
g ( x)  x 2  4
f
(3)
g
5) 
at x  0, g( x  3)
For each of the following pairs of functions, find: a. ( f  g)(x)
12.) f (x)  x  2
f 
 6
g
4) ( f  g )(1)
Determine the following.
5. ( j  h)( x)
3
, j ( x )  3 x  5 , k ( x)  x  5 . Determine the following.
x2
11. ( g f )( x )
12. j ( h( x))
14. h( j ( x))
15. f (k(x))
f ( x)  x 2  3 , g ( x )  x  1 , h( x ) 
10. f (g (3))
13. k ( f ( 4))
III. Use the graphs from yesterday (top of this page) to answer the following questions.
16. ( f  g )( 2)
17. g ( f (3))
18. ( f ( g (3))
V. The following are composite functions. Find f (x) and
19.
h(x)  x 2  3
20.
g(x) so that h(x)  f (g(x)) .
h( x)  (2 x  1) 3
g(x) are inverses by using composition of functions.
x
g ( x) 
22. f ( x)  7 x  1
2
g ( x)  9  x
24. f ( x)  3 1  x
VI. Determine if f (x) and
21. f ( x)  2 x
23.
f ( x)  9  x 2
x 1
7
g ( x)  1  x 3
g ( x) 
p.8
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) f ( x )  4 x  6
2) d ( x )  x  4
3) g ( x )  x 3  1
4) v ( x )  x  2
5) h( x)  ( x  3) 2
6) y  2  x
II. Find the inverse of each relation. State the domain and range. Is the inverse a function. State why or why not.
7) (1,5), (3,3), (4,2)
8) (a, c), (a, d ), (b, e), (b, g )
10) y  x 2
11) v ( x ) 
1
3x
9) f ( x )  3x  2
12) y  2 x
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.
1
x
4
g( x)  x  2
g( x) 
13) f ( x )  4 x
15) f ( x )  x 2  2
14) f ( x )  2 x  5
g( x)  2 x  5
16) f ( x )   x  7
g( x)   x  7 IV.
IV For each graph do the following
a) Restrict the domain to x  0 . Sketch the original and the inverse on the same graph in different colors.
b) Restrict the domain to x  0 . Sketch the original and the inverse on the same graph in different colors.
17)
18)
19)
Sept. 19th – 20th, 2012
HOMEWORK
20)
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)
y  x2  3
2)
y  ( x  2)2
3)
6)
y  x 3
7)
y  3 x 1  2
8) y 
II. Given f ( x )  3x  5 ,
y  4 x3
2
x 1
4) y 
1
x 1
4
9) y  3 x  1
5)
y  ( x  3)3
10) y 
1
x 2
2
g ( x )  x 2  1 , and h( x)  x 2  2 x  1 find the following.
g
h
11) f  g
12)
15) f  g
16) h  g (2)
13) ( g  f )( 2)
14) ( fh)( 2)
17) h( f ( 2))
18) h( f ( x ))
p.9
NOTES
Sept. 21st, 2012
Difference Quotient Worksheet
I. For the given function find the requested value.
1) f ( x )  2 x  11 , find f (8)
2)
g (a )  a 2  4a  7 , find g($)
3)
f ( x)  10 x 2  11x  4 , find  f ( x )
II. For each given function, find f ( x  h ) .
4) f ( x )  5x  8
5)
f ( x )  7 x 2  3x  1
III. For each given function, find f ( x  h )  f ( x ) .
6) f ( x )  5x  8
7)
IV. For each given function, find
8) f ( x )  5x  8
H0MEWORK
f ( x )  7 x 2  3x  1
f ( x  h)  f ( x )
. Simplify your results.
h
2
9) f ( x )  7 x  3x  1
Sept. 21st, 2012
10) f ( x )  3x  5
Difference Quotient Worksheet
I. For the given function find the requested value. Use separate paper or back of sheet 9.
1)
h(n)  n2  3n  8 , find h( 4)
2)
g ( x)  2 x 2  5 , find g (2a )
3) f ( x )  5x  8 , find  f ( x )
II. For each given function, find f ( x  h ) .
4) f ( x)  2 x  5
5)
f ( x)  x 2  x  5
III. For each given function, find f ( x  h )  f ( x ) .
6) f ( x)  2 x  5
IV. For each given function, find
8) f ( x)  2 x  5
7)
f ( x)  x 2  x  5
f ( x  h)  f ( x )
. Simplify your results.
h
2
9) f ( x )  x  x  5
10.) f ( x)  4 x  9
p.10