MATH 1051 Exam 4 Review
1.
2.
3.
Find the domain of f (x):
f (x) =
log2 (x 2)
x 5
f (x) =
p
log(x + 5)
Find the domain of f (x):
Find the domain of f (x):
f (x) =
ln(x 5)
x+1
4.
5.
Let f (x) =
p
Let f (x) =
x + 2 and let g(x) = x3 + 6. Findf (g(2)) and simplify your answer.
x 3
x2 2
and let g(x) = 10x . Findf (g(log 5)) and simplify your answer.
6.
Find the domain of f (g(x)), where
x+1
and
x 2
p
g(x) = x + 6.
f (x) =
7.
Find the domain of f (g(x)), where
f (x) = log3 (x) and
g(x) = x3
3.
8.
Graph f (x) = e x 3 Label the asymptote and at least one point on your graph.
You may use as many of the provided axes as you choose, but be clear which is your final
graph of f (x).
9.
Graph f (x) = 3x+1 + 5. Label the asymptote and at least one point on your
graph. You may use as many of the provided axes as you choose, but be clear which is
your final graph of f (x).
10.
Graph f (x) = log2 (x 2) 1. Label the asymptote and at least one point on
your graph. You may use as many of the provided axes as you choose, but be clear which
is your final graph of f (x).
11.
The graph of g(x) is shown. Draw the graph of g 1 (x)
µ
6)
,
:#
t5 , 5)
-
⇐
12.
"
•
: *N
Use the graph to determine whether each function is one-to-one:
a. y = f (x)
its
<
"
b.y = g(x)
>
c. y = h(x)
in
⇐
es, 0 )
y
13.
Find the exact value of each logarithm or state that it is undefined.
a. log2 (64)
b. log5 (5)0
c. log1 7(1)
d. log(1, 000)
e. log7 (7105 )
f. ln(e9 )
g. log5 (0)
h. ln( 2)
1
i. log4 ( 16
)
5
j. logp3 (3 2 )
1
k. log1 9( 19
)
p
l. ln( e)
m. log8 (2)
14.
15.
16.
f (x) = log3 (x + 1)
1. Find f
f (x) = 1 + x5 . Find f
f (x) =
x+1
.
2x 3
Find f
1
1
(x).
(x).
1
(x).
See
for
17.
P.
log
rules
3) = 3
Solve for x:
ln(x + 1)
19.
,
Solve for x:
log3 (x + 1) + log3 (x
18.
302
ln(x
3) = 2
Solve for x:
8 = 3 log(10x) + 2 log(x)
Properties
to
of
memorize
logarithms
.
,
20.
Approximate the value of log3 (439) using the change of base formula. Write
down the formula that you enter into your calculator.
21.
Approximate the value of log2 (41) using the change of base formula. Write down
the formula that you enter into your calculator.
22.
Solve for x:
e2+3x = (e2 )4
23.
Solve for x:
24.
Solve for x:
5x = 125(x
2 +1)
ex+1 = 7
25.
A population of deer follows a logistic growth model,
P (t) =
100
,
1 + 4e 0.5t
where P (t) is the number of deer in the population after t years.
a. Find the initial population size (i.e. the number of deer at time t = 0)
b. When will the population reach 75 deer?
26.
A population of rabbits obeys the law of uninhibited growth,
N (t) = N0 ekt ,
where N is the number ofrabbits present, t is time in months, and N0 (initial number)
and k (growth rate) are constants particular to this population of rabbits.
If there are 30 rabbits present initially and 90 rabbits present after 2 months, how many
rabbits will be present after 6 months?
27.
A culture of bacteria obeys the law of uninhibited growth,
N (t) = N0 ekt ,
where N is the number of bacteria present, t is time in hours, and N0 (initial number)
and k (growth rate) are constants particular to this bacterial culture.
If there are 100 bacteria present in the culture initially and 500 bacteria present after 1
hour, at what point will there be 2,000 bacteria present?