Precalculus HS Mathematics

Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 13 of 98

Functions: Give One, Get One (pp. 1 of 2)

Under each representation, answer the true-false questions that follow. Then, provide additional �true� statements about the function.

Sam

ple

A)

True or False?

____ 1. One of the function�s y-intercepts falls between 6 and 7.

____ 2. f(2) is equal to f(4).

____ 3. f(6) is greater than f(5).

____ 4. The function reaches a maximum value at x = 3.

____ 5. The domain of f(x) is {x x }.

____ 6. The range of f(x) is is (- , 5.5].

True or False? ____ 1. The y-intercept of this function is 0.

____ 2. The domain of g(x) can be described as 0 x 10.

____ 3. Between x = 2 and x = 4, the function has a slope of ½.

____ 4. The function reaches a minimum value at x = 8.

Write another valid statement about the function:

Write another valid statement about the function:

Also, ____________________ told me this:

Also, ____________________ told me this:

Precalculus HS Mathematics

Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 14 of 98

Functions: Give One, Get One (pp. 2 of 2)

Under each representation, answer the true-false questions that follow. Then, provide additional �true� statements about the function.

B)

The graph shows the temperature (y, in F) over a period of 24 hours.

C)

The graph shows the population (y, in

thousands of people) over a 10-year period.

True or False?

____ 1. The temperature ranged from 40 F to 80 F.

____ 2. The temperature was dropping during the first 10 hours shown.

True or False? ____ 1. The population reached a

maximum around x = 4.5 years. ____ 2. The population was increasing

between 0 and 10 years.

Write two more valid statements about the function:

Write two more valid statements about the function:

Also, ____________________ told me this:

Also, ____________________ told me this:

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Precalculus HS Mathematics

Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 27 of 98

End Behavior (pp. 1 of 2)

Enter each function into a graphing calculator to determine its behavior on the extreme left (x - ) or right (x ) of the graph. Identify the end behavior (A, B, or C) exhibited by of each side of the graph of the given function. If the end behavior approaches a numerical limit (option B), determine this numerical limit. 1) Function: xxf 3)(

As x - , what does the function do?

A) )(xfB) nxf )( (n = ____ ) C) )(xf

AB

C

A

B

C

As x , what does the function do?

A) )(xf B) nxf )( (n = ____ ) C) )(xf

2) Function: 2

3)( xxfAs x - ,

what does the function do?

A) )(xfB) nxf )( (n = ____ ) C) )(xf

A

B

C

A

B

C

As x , what does the function do?

A) )(xf B) nxf )( (n = ____ ) C) )(xf

3) Function:

1)( 2x

exfx

As x - , what does the function do?

A) )(xfB) nxf )( (n = ____ ) C) )(xf

A

B

C

A

B

C

As x , what does the function do?

A) )(xf B) nxf )( (n = ____ ) C) )(xf

4) Function:

xexf

12)(

As x - , what does the function do?

A) )(xf B) nxf )( (n = ____ ) C) )(xf

A

B

C

A

B

C

As x , what does the function do?

A) )(xf B) nxf )( (n = ____ ) C) )(xf

Precalculus HS Mathematics

Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 28 of 98

End Behavior (pp. 2 of 2)

For each function, complete the table. Using the table, describe the behavior of the function by both completing the blank and selecting the best multiple choice answers.

5) 5213)(

xxxf

x y = f(x) 500

1,000

1,500

End Behavior:

As x , what does the function do? ______________________

This means that the function _____________ as you move to the _____________ . A) points up

B) flattens out C) points down

D) left of the graph E) middle of the graph F) right of the graph

6) 857)(

2

xxxf

x y = f(x) -2,000

-4,000

-6,000

End Behavior:

As x - , what does the function do? ______________________

This means that the function _____________ as you move to the _____________ . A) points up

B) flattens out C) points down

D) left of the graph E) middle of the graph F) right of the graph

7) xxexf )(

x y = f(x) 50

60

70

End Behavior:

As x , what does the function do? ______________________

This means that the function _____________ as you move to the _____________ . A) points up

B) flattens out C) points down

D) left of the graph E) middle of the graph F) right of the graph

Precalculus HS Mathematics

Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 31 of 98

Even and Odd (pp. 1 of 2)

The given functions appear to behave in a similar fashion, but each is only partially graphed. Complete the tables and sketch the remainder of each graph.

24 8.43.0)( xxxf 35 6.11.0)( xxxg

x y -4 -3 -2 -1 0 0 1 -4.5 2 -14.4 3 -18.9 4 0

x y -4 -3 -2 -1 0 0 1 -1.5 2 -9.6 3 -18.9 4 0

Questions 1. How do the tables of the two functions (f(x) and g(x)) differ?

2. How do the graphs of the two functions (f(x) and g(x)) differ?

3. One function is referred to as being �even� and the other is considered �odd.� Which do you think is which? Why?

Precalculus HS Mathematics

Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 32 of 98

Even and Odd (pp. 2 of 2)

Here, the functions have been changed to include �+5.� As before, complete the tables and sketch the remainder of each graph.

58.43.0)( 24 xxxh 56.11.0)( 35 xxxk

x y -4 -3 -2 -1 0 5 1 0.5 2 -9.4 3 -13.9 4 5

x y -4 -3 -2 -1 0 5 1 3.5 2 -4.6 3 -13.9 4 5

Questions 4. Which function, h(x) or k(x) is even? To which of the previous functions is this even function

related, f(x) or g(x)? What characteristics do these functions have in common?

5. Unlike function g(x), k(x) can not be considered �odd.� Why not? How are functions g(x) and k(x) different?

Precalculus HS Mathematics

Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 35 of 98

Function Practice (pp. 1 of 2)

1) Tell the domain and range of each function, using both set notation and interval notation. A) B)

Set

Notation Interval Notation

Domain {x 0 x 8} [0, 8]

Range

Set Notation

Interval Notation

Domain

Range

C) 32 2xy

(Sketch graph)

D) xy 2

(Sketch graph)

Set Notation

Interval Notation

Domain {x x }

Range

Set Notation

Interval Notation

Domain

Range

2) Tell the intervals on which the function is increasing and decreasing. A) B)

Increasing

Decreasing (5, 6)

Increasing

Decreasing

Precalculus HS Mathematics

Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 36 of 98

Function Practice (pp. 2 of 2)

3) Use a calculator to sketch the graph of each function. Then, find the coordinates for any maximum and minimum points on each graph. Finally, tell the intervals on which the function is increasing and decreasing.

A) 52)( 2 xxxf B) 34)( 23 xxxf C) 2

52)(2

xxxxf

Maximum: Maximum: Maximum:

Minimum: Minimum: Minimum:

Increasing: Increasing: Increasing:

Decreasing: Decreasing: Decreasing:

4) Use a calculator to complete the tables. Describe the end behavior of each function.

A) x

xxf 5)( x f(x)

B) xxxf

25)( x f(x)

-100 80

-150 90

-200 100

As x ______ As x ______

The function f(x) ______ The function f(x) ______

5) Which of the functions from exercise #4 has a horizontal asymptote? 6) Use a calculator to sketch the graph of each function. Then tell whether each function is even,

odd, or neither, and explain why.

A) xxf )( B) xxxf 4)( 2 C) 4

)( 2

3

xxxf

Precalculus HS Mathematics

Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 39 of 98

Parent Function Checklist (pp. 1 of 2)

For each parent function, identify the �type� using a phrase from the word bank at the right. Then, use a calculator to help sketch the graph of each function.

Parent Function Graph Word Bank (Types)

1) xxf )(

Absolute Value

Type:

Exponential (decay)

2) 2)( xxf

Exponential (growth)

Type:

Linear

3) xxf 2)(

Logarithmic

Type:

Rational

4) xxf 21)(

Quadratic

Type:

5) xxf )(

Type:

6) xxf 1)(

Type:

7) ( ) log ( )bf x x

Type:

Precalculus HS Mathematics

Unit: 01 Lesson: 01

© 2009, TESCCC 08/10/09 page 40 of 98

Parent Function Checklist (pp. 2 of 2)

Determine whether each function possesses each of the given properties. If not, mark out the box. If so, use the codes in the correct boxes to spell the message at the bottom of the page. xxf )( 2)( xxf xxf 2)( xxf 2

1)( xxf )( xxf 1)( ( ) log( )f x x

The domain of the function is (-

, ) 11 T 1 A 26 U 9 T 32 E 19 H 27 R

The range of the function is (0, ) 12 M 6 M 31 R 14 E 18 A 11 N 28 M

The range of the function is [0, ) 7 R 4 T 9 D 1 F 7 N 4 Y 12 Y

f(x) is increasing when x < 0 13 M 29 Y 15 Y 15 G 24 B 5 V 6 U

f(x) is decreasing when x < 0 13 T 18 E 14 J 19 H 30 H 5 O 32 T

f(x) is increasing when x > 0 12 R 3 E 27 E 12 B 28 G 13 H 16 A

f(x) is decreasing when x > 0 29 B 14 A 21 A 10 E 17 M 29 H 14 S

f(x) has a vertical asymptote at x =

0 4G 2 C 16 T 4 T 23 U 2 M 22 V

f(x) has a minimum at x = 0 22 L 6 L 21 E 7 V 24 B 15 D 30 A

As x , f(x) 0. 10 M 11 D 3 E 20 T 8 C 25 I 9 E

The function is even 20 W 8 N 11 R 31 Y 17 R 16 M 25 I

The function is odd 23 L 19 E 20 H 26 F 17 P 21 T 18 L

�If you 20 14 23 6 9 30 18 21 12 26 20 29

You don�t

19 1 22 32 4 5 T

17 3 13 27 2 24 10 31 16 7 15 11 30 25 8 28 �Mark Twain