Download 1) Find the smallest value in the domain of the function 0РBС œ #B

Calculus 118
Test 1, September, 2000
Show all necessary work in the space provided with each question.
Page 1
1) Find the smallest value in the domain of the function 0 ÐBÑ œ È#B & Þ
A) 2
B) &#
C) 5
D) #&
E) #
F) 1
G) 0
H) &
2) Find the domain of the function 1ÐBÑ œ
A) Ð _ß "Ñ Ð "ß _Ñ
C) Ð _ß "Ñ
E) Ð _ß "Ñ
G) Ð "ß "Ñ
"B
"B
Þ
B)
D)
F)
H)
Ð _ß "Ñ Ð"ß _Ñ
Ð "ß _Ñ
Ð"ß _Ñ
Å
3) Which of the following are graphs of functions?
A) I, II only
D) III, V only
I
II
III
IV
V
VI
B) I, II, III only
E) I, II, IV, VI only
C) I, II, III, IV, VI only
F) all of them
4) Relative to the graph of C œ B# , the graph of C œ ÐB #Ñ# is changed in what way?
A) shifted 2 units upward
B) compressed vertically by a factor of 2
C) compressed horizontally by a factor of 2
D) shifted 2 units to the left
E) shifted 2 units to the right
F) shifted 2 units downward
G) Stretched vertically by a factor of 2
H) stretched horizontally by a factor of 2
$
5Ñ We can describe the function 0 ÐBÑ œ È
B as
I: even
II: odd
A) I only
D) I and III only
B) II only
E) II and III only
III: one-to-one
C) III only
F) None of these
#
6) We can describe the function 0 ÐBÑ œ eB # as
I: even
II: odd
III: one-to-one
A) I only
D) I and III only
B) II only
E) II and III only
C) III only
F) None of these
7) A bacteria culture starts with 200 bacteria and triples in size every half hour. After
Calculus 118
Test 1, September, 2000
Show all necessary work in the space provided with each question.
2 hours, how many bacteria are there?
A) 17,800
B) 16,200
C) 23,500
E) 19ß 300
F) 14,800
G) 15,700
Page 2
D) 24,000
H) 21,000
B
8) For what value of B is #B œ ˆ "# ‰ ?
A) È#
B) #
C) È#
D) #
E) "
F) !
"
G) #
H) "
9) Which of the following statements are true about the graph of the function
C œ $B * ?
i) It has no vertical asymptote.
ii) It has no horizontal asymptote.
iii) It has a y-intercept at #Þ
iv) It has an B-intercept at 2.
A) i) only
D) iv) only
B) i), iii) and iv) only
E) ii) and iii) only
10) Find the inverse function for 0 ÐBÑ œ #B &Þ
A) 0 " ÐBÑ œ B &#
B) 0 " ÐBÑ œ B œ &#
C) 0 " ÐBÑ œ B# &
D) 0 " ÐBÑ œ B&
#
E) 0 " ÐBÑ œ #B & F) 0 " ÐBÑ œ #B &
G) 0 " ÐBÑ œ B&
H) 0 " ÐBÑ œ B# &
#
11) Find the value of
A) "
D) "!#
G) #
log # "Þ
B) "#
E)"
H) #
C) !
F) "#
12) Find the value of
A) "#
D) "
G) ")
log "' #Þ
B) #
E) $
H) "%
C) %
F) !
13) Find the value of
A) !
D) $
G) *
log $ a$# b ".
B) "
C) #
E) È$
F) #)
H) "!
1%) Find the value of a log $ $b# ".
A) !
B) "
C) #
C) ii), iii) and iv) only
F) i) and iv) only
Calculus 118
Test 1, September, 2000
Show all necessary work in the space provided with each question.
E) È$
H) "!
F) #)
1&) Find the value of
A) #$
D) $#
G) #/
$
lnÈ/$ Þ
B) È/
E) /$
H) /#$
C) /#
F) /$ #
16) Find the value of
A) #
D) /"'
G) #
/
log # / log # "'
Þ
B) /#
C) %
E) %
F) /#
"'
H) /
D) $
G) *
$
17) Simplify: 2$ )' %'
A) '%$
B) #$
C) %$
D) )$
E) "
F) #"$
G) #*
H) #
18) Solve the equation: log % B œ $# Þ
19) Solve the equation: 2 ln (B $Ñ ln ÐB "Ñ œ $ ln #Þ
20) Rewrite the expression using just one logarithm.
& log + B "# log + Ð$B %Ñ $ log + Ð&B "Ñ
#"Ñ Given the functions 0 ÐBÑ œ #B# B and 1ÐBÑ œ %B $ß then 0 91 œ
A) $#B# %%B "&
Page 3
Calculus 118
Test 1, September, 2000
Show all necessary work in the space provided with each question.
Page 4
B) $#B# )B '
C) $#B# %B "&
D) $#B# %)B ")
E) None of these
2#) Find the inverse of the function 0 ÐBÑ œ ln ÐB $ÑÞ
2$) Given the function 0 ÐBÑ œ
$
B"
ß
A) Find the inverse, 0 " ÐBÑÞ
B) What is the domain of 0 ?
C) What is the domain of 0 " ?
D) What is the range of 0 ?
E) What is the range of 0 " ?
#%) Which is the most appropriate viewing rectangle for 0 ÐBÑ œ 'B# B "! ?
A) Ò &!ß &!Ó ‚ Ò &!ß &!Ó
B) Ò !ß "!Ó ‚ Ò !ß "!Ó
C) Ò &ß &Ó ‚ Ò &ß &Ó
D) Ò "!ß "!Ó ‚ Ò !ß "!Ó
E) Ò &ß &Ó ‚ Ò "!ß "!Ó
F) Ò &ß "!Ó ‚ Ò !ß "!Ó
#&) Determine the number of real solutions of the equation &B% $B# œ "!B& B$ &
A) 0
B) 1
C) 2
D) 3
E) 4
F) 5
G) 6
H) 7