Hi y'all! If you could answer any of the questions here that would be AWESOME

/tmp/282676-14774105227098708-32654-96170.dvi

Express the function f(x) = x+8

x5 as a piecewise-defined function by eliminating

as its graph on [6, 6]? x2 1

the absolute value signs.

x 5 x+8, (,8)(5,),

1. f(x) =

2.f(x) =

1.y=|x+1|, x=1 2

5 x, [8, 5] x+8

2.y=|x1|, x=1 x1

x 5 x+8, (,5)(8,),

x2 1 3.y=|x1|, x=1

2

5.y=|x21|, x=1 x1

6.y=x21, x=1 |x + 1|

003 10.0 points

Which one of the following functions has

5 x, (5, 8) x + 8

4.y=x1, x=1 |x 1|

5x 3.f(x)=x+8,

5x, 4. f(x) = x+8

(, 8) (5, ), (8, 5]

(,8)(5,), [8, 5]

(, 8) (5, ), (8, 5]

002 10.0 points

x 5 , x+8

6

4

2 3

6

9

9

6

3

2

4

6

x 5 , x+8

x 5 , 5. f(x) = x+8

5 x , x+8

Which one of the following functions has

sivilay (eas3995) - HW 13: More PW Functions, Limits - hager - (53355) 2

Hint: draw the graph. 1. (, 3) 2. (, 3) 3. (3, 3)

4. (3,) 5. (,3), (3,) 6. (3, ) 7. no interval

006 10.0 points

Find all intervals on which

f(x) = |x+4||x4| is constant and positive.

Hint: draw the graph. 1. no interval 2. (4, ) 3. (4, )

4. (, 4) 5. (,4), (4,) 6. (, 4) 7. (4, 4)

007 10.0 points

as its graph on [8, 8]? 1. y = x29, x=3

|x 3| 2. y = |x29|, x=3

x+3 3. y = |x29|, x=3

x3 4. y = |x29|, x=3

x3 5. y = x29,

|x + 3| 6. y = |x29|,

x+3 004

x=3 x=3

10.0 points

Find all intervals on which f(x) = |x+2||x2|

is increasing. Hint: draw the graph.

1. no interval 2. (,2), (2,) 3. (, 2) 4. (2, ) 5. (, 2) 6. (2, ) 7. (2, 2)

005 10.0 points

Find all intervals on which f(x) = |x3||x+3|

is decreasing.

Below is the graph of a function f.

sivilay (eas3995) - HW 13: More PW Functions, Limits - hager - (53355) 3

6

4

2 2

4

6

6

4

2

2

4

6

5. lim f(x) = 1 xb

009 10.0 points

Below is the graph of a function y = f(x) 10

9 8 7 6 5 4 3 2 1 0

-1 -2 -3 -4 -5

Use the graph to determine lim f(x).

x1+

1. limit = 1 2. limit = 0 3. limit does not exist 4. limit = 4 5. limit = 2

010 10.0 points

Below is the graph of a function f. 10

x9 8

6

4

2 2

8

6

4

2

4

2

4

6

Use this graph to determine the value of lim f(x).

x5

1. limit = 3 2. limit = 7 3. limit = 4 4. limit = 4 5. limit does not exist

008 10.0 points

The graph of the function f is shown in the figure.

y

3 2 1

Oab

6

4

2

8

6

4

2

2

4

2

4

6

7 6 5 4 3

1

0 -1 -2 xa -3 -4 -5

Which of the following statements about f is true?

1. lim f(x) = 2 xb 2

2. lim f(x) = lim f(x) xa xb

3. lim f(x) = 2

4. lim f(x) does not exist. xa

sivilay (eas3995) - HW 13: More PW Functions, Limits - hager - (53355)

4

6

4

2 2

8

6

4

2

4

2

4

6

Use the graph to determine lim f(x).

x3

1. limit = 18 2. limit = 6 3. limit = 8 4. limit does not exist 5. limit = 3

011 10.0 points

Below is the graph of a function f. 10

9 8 7 6 5 4 3 2 1 0

-1 -2 -3 -4 -5

Use the graph to determine lim f(x).

x2

1. limit = 2
2. limit = 4
3. limit does not exist
4. limit = 3
5. limit = 4

012 10.0 points

Below is the graph of a function f.

10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5

Use the graph to determine

1. lim x 5

2. lim x 5

3. lim x 5

4. lim x 5

5. lim x 5

lim

f(x).

x 5 does not exist

f (x) f(x)=8 f(x)=5 f(x)=7 f(x)=6

013 10.0 points

6

4

2 2

8

6

4

2

4

2

4

6

When f is the function defined by f(x)= 3x8, x<1,

determine if

5x9, x1, lim f (x)

x1 exists, and if it does, find its value.

1. limit = 5 2. limit = 6 3. limit = 7 4. limit = 4 5. limit = 3

sivilay (eas3995) - HW 13: More PW Functions, Limits - hager - (53355) 5

6. limit does not exist

If f is defined piecewise for x = 0 by

5 + 1x, 2

3x,

x < 2, 2x<0

014

10.0 points

Answer this one in decimal form, not fraction form.

f(x) =

2

L e t f b e t h e f u n c t i o n d e fi n e d b y f(x)= x5.

1 determine all values of a at which

or 0 2 .

lim f (x) xa

exists, expressing your answer in interval no- tation.

1. (,2)(2,) 2. (, 2)(2, 0)(0,2)(2,) 3. (, 0)(0, 2)(2,) 4. (,0)(0,) 5. (, 2)(2, 0)(0,) 6. (, 2)(2, 2)(2,) 7. (,2)(2,)

017 (part 1 of 2) 10.0 points

a) Find the domain of f(x) = 10x2

x + 6 1. All real numbers except x = 0

2. All real numbers except x = 6 3. All real numbers except x = 10 4. None of these 5. All real numbers except x = 6 6. All real numbers except x = 10

x2 25 By computing the values of f at

andat estimate the value of

4.9, 4.99, 4.999 , 5.1, 5.01, 5.001,

015

lim f(x). x5

10.0 points

Consider the function 2 x ,

f(x) = x, (x 3)2,

x < 1 1x<2 x 2 .

Find all the values of a for which the limit lim f (x)

xa exists, expressing your answer in interval no-

tation. 1. (, 1) (1, ) 2. (, 2) (2, ) 3. (, ) 4. (,1)(1,2)(2,) 5. (, 1] [2, )

016 10.0 points

sivilay (eas3995) - HW 13: More PW Functions, Limits - hager - (53355) 6

018 (part 2 of 2) 10.0 points

b) Identify any vertical and horizontal asymp- totes.

1. x = 6 2. None of these 3. x = 6, y = 10 4. x = 10 5. x = 6, y = 6 6. x = 10

019 (part 1 of 4) 10.0 points

f(x) = 3 10. x2

a) Find all x-intercepts.

1. (0, 0)

2. 10,0 3

3. None of these 4. (3, 0)

5. 10,0 3

020 (part 2 of 4) 10.0 points

b) Find the y-intercept if there is one.

1. (0, 0)

2. 0,10 3

3. None of these 4. (0, 3)

021 (part 3 of 4) 10.0 points

c) Find all vertical asymptotes. 1. x = 1

2. x = 0 3. x = 10 4. None of these

022 (part 4 of 4) 10.0 points

d) Find all horizontal asymptotes. 1. y = 1 2. y = 3 3. None of these

4. y = 0 023 (part 1 of 2) 10.0 points

Given the graph f(x) = ex + 4

a) Identify the horizontal aymptote. 1. y = 0 2. y = 1 3. y = 4

4. None of these 5. y = 4 6. y = 1

024 (part 2 of 2) 10.0 points

b) Identify the shift for the graph 1. up 4 units 2. left 4 units 3. right 4 units

4. No shift 5. down 4 units

sivilay (eas3995) - HW 13: More PW Functions, Limits - hager - (53355) 7

025 (part 1 of 2) 10.0 points

3. f(x) oscillates around the limit as x

029 (part 3 of 4) 10.0 points

c) Find the limit of the function f(x) as x .

030 (part 4 of 4) 10.0 points

d) Is f(x) greater or smaller than the above limit as x ?

1. Greater 2. f(x) oscillates around the limit as x

3. Smaller 031 (part 1 of 2) 10.0 points

a) Find the domain of f(x)=13x

1+8x 1. All real numbers except x

2. None of these 3. All real numbers except x

4. All real numbers except x 5. All real numbers except x

6. All real numbers except x

= 1

= 0

=1 8

=1 8

=2

026 (part 2 of 2) 10.0 points

b) Identify any vertical and horizontal asymp- totes.

Given the function f(x)= 4x

1. None of these 2. x = 1, y = 3

and the graph

x2 1 6

2

8

6

4

22

4

2

4

6

4

6

8

88 3. x = 1, y = 1

4. x = 1, y = 3 88

5. x = 3, y = 8 6. x = 8, y = 0

027 (part 1 of 4) 10.0 points

a) Find the limit of the function f(x)= 2x1

a) Use the tables of values x f(x) x f(x) x f(x) 0.5 1.001 5 0.9 1.01 10 0.99 1.1 100 0.999 1.5 1000

to determine the vertical and horizontal asymptotes of the function.

1. x = 1 and x = 1, y = 0 2. None of these

as x .

x3

028 (part 2 of 4) 10.0 points

b) Is f(x) greater or smaller than the above limit as x ?

1. Greater 2. Smaller

sivilay (eas3995) - HW 13: More PW Functions, Limits - hager - (53355) 8

3. x = 3 and x = 3, y = 2 4. x = 4 and x = 4, y = 3 5. x = 5 and x = 5, y = 4 6. x = 2 and x = 2, y = 1

032 (part 2 of 2) 10.0 points

b) Find the domain of the function. 1. All real numbers except x = 3 2. All real numbers except x = 2 3. All real numbers except x = 0 4. None of these

5. All real numbers except x = 1 6. All real numbers except x = 1

033 (part 1 of 4) 10.0 points

Consider 1 2x f(x)= 1x.

a) Find the x-intercept. 1. 1 , 0

3. 1 , 0 2

4. None of these 5. (2, 0)

034 (part 2 of 4) 10.0 points

b) Find the y-intercept. 1. (0, 1) 2. (0, 2)

3. 0,1 2

4. None of these 035 (part 3 of 4) 10.0 points

c) Find the vertical asymptote. 1. x = 2 2. None of these 3. x = 1

4. x = 0 036 (part 4 of 4) 10.0 points

d) Find the horizontal asymptote. 1. y = 1 2. y = 2 3. None of these

4. y = 0 037 (part 1 of 4) 10.0 points

a) Find the limit of the function f(x)= 2x1

2 2. (2, 0)

038 (part 2 of 4) 10.0 points

b) Is f(x) greater or smaller than the above limit as x ?

1. Greater

2. Smaller

3. f(x) oscillates around the limit as x

039 (part 3 of 4) 10.0 points

c) Find the limit of the function f(x) as x .

040 (part 4 of 4) 10.0 points

d) Is f(x) greater or smaller than the above limit as x ?

as x .

x2 + 1

sivilay (eas3995) - HW 13: More PW Functions, Limits - hager - (53355) 9

1. Smaller 2. f(x) oscillates around the limit as x

3. Greater 041 (part 1 of 4) 10.0 points

2. None of these 3. y = 1 4. y = 0

045 (part 1 of 4) 10.0 points

Consider f(x)= 1 .

Consider f(x) = 3x .

x 1 a) Find the x-intercept.

x24x12 a) Find the x-intercept.

1. (1, 0) 2. None of these 3. (1, 0) 4. (1, 0)

042 (part 2 of 4) 10.0 points

1. (0, 0) 2. (6, 0) 3. (2, 0) 4. (2, 0) 5. None of these

046 (part 2 of 4) 10.0 points

b) Find the y-intercept. 1. (0, 0) 2. (0, 6) 3. None of these

4. (0,2) 047 (part 3 of 4) 10.0 points

c) Find the vertical asymptote(s). 1. x = 2 2.x=6, x=2 3. x = 0

4. None of these 5. x = 6

048 (part 4 of 4) 10.0 points

d) Find the horizontal asymptote.

b) Find the y-intercept. 1. 0, 1

1 2. None of these

3. (0, 1) 4. 0,1

1

043 (part 3 of 4) 10.0 points

c) Find the vertical asymptote. 1. None of these 2.x=1 3. x = 0

4. x = 1 044 (part 4 of 4) 10.0 points

d) Find the horizontal asymptote. 1. y = 1

4. y = 2 5. y = 1 6. y = 0

053

10.0 points

5. x = 2 6. There are no vertical asymptotes.

055 10.0 points

Find the vertical asymptotes (if any) of

f(x) = x3 + 1 x+1

sivilay (eas3995) - HW 13: More PW Functions, Limits - hager - (53355) 10 Find the vertical asymptotes (if any) of

1. None of these 2. y = 3 3. y = 0 4. y = 1

049 (part 1 of 4) 10.0 points

Consider f(x) = 2x . x2 + 4

What is the x-intercept? 050 (part 2 of 4) 10.0 points

What is the y-intercept? 051 (part 3 of 4) 10.0 points

What is the vertical asymptote? 1. x = 3 2. x = 3 3. None of these

4. x = 0 5. x = 2 6. x = 2

052 (part 4 of 4) 10.0 points

What is the horizontal asymptote? 1. None of these 2. y = 2 3. y = 1

f(x)= x22 x2 x 2

1. x = 2 2. x = 1, x = 2 3. x = 2 4. x = 1, x = 2 5. No vertical asymptotes exist. 6. x = 1, x = 2 7. x = 1, x = 2 8. x = 1 9. None of these

10. x = 1

Identify the vertical asymptote(s) of

g(x) =

1. y = 0 2. x = 2, x = 7

3. x = 9 4. x = 7

x 7 . x2 9x+14

054 10.0 points

sivilay (eas3995) - HW 13: More PW Functions, Limits - hager - (53355) 11

1. x = 0, x = 1 2. x = 1 3. x = 0 4. x = 1

5. None of these 6. No vertical asymptotes exist. 7. x = 1 8. x = 0, x = 1

056 10.0 points

Determine whether f (x) = x2 1

x+1 has a vertical asymptote or a removable dis-

continuity at x = 1. 1. Vertical asymptote 2. Removable discontinuity 3. Neither

057 10.0 points

Find all vertical asymptotes of the graph of y = 3x2+x4.

x2 3x+2 1. x = 2, 1

2. x = 1 3. x = 2, 1 4. x = 2 5. x = 2, 1