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WorksheetsChapter 4: Exponential and Logarithmic Functions
Total questions: 38
Worksheet time: 2hrs 49mins
Name
Class
Date
1.
What is a, the starting term, for the function: f(x) = 300(1.16)x?
a)
300
b)
1.16
c)
.16
d)
x
2.
The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the decay factor?
a)
.08
b)
1.08
c)
.92
d)
8
3.
Which of the following functions shows an initial amount of $15 and an increase of 35% each year?
a)
y = 15(35)x
b)
y = 15(1.35)x
c)
y = 15(0.35)x
d)
y = 35(1.15)x
4.
Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)6
A=1200(.85)6
a)
Growth
b)
Decay
5.
Is the pictured graph growth, decay, or linear or none?
a)
Exponential Growth
b)
Exponential Decay
c)
Linear
d)
None
6.
Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.
a)
y=5000(0.7)x
b)
y=30(5000)x
c)
y=5000(1.3)x
d)
y=5000xx
7.
What type of function is y = 7(5/4)x?
a)
Exponential Growth
b)
Exponential Decay
c)
Linear
d)
None of the above
8.
Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?
a)
$23,219.72
b)
$136.72
c)
$51,710.94
d)
$16,710.94
9.
Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased about 5% per year. How much is the home worth today?
a)
$176,783.29
b)
$424,527.63
c)
$57,357.75
d)
$532,041,076.80
10.
Are the following inverses of each other?
a)
True
b)
False
11.
What is the equation that the inverse will reflect across?
a)
y = x
b)
y = 0
c)
x = 0
d)
Potato
12.
a)
Inverse Functions
b)
Not Inverse Functions
13.
Find the inverse of f(x) = x2 - 5
a)
f-1(x) = √(x) + 5
b)
f-1(x) = ∛(x-5)
c)
f-1(x) =√(x+5)
d)
f-1(x) = x2 - 5
14.
Was the inverse function found correctly?
a)
no,
b)
yes
15.
log a a =
a)
10
b)
0
c)
1
d)
-1
16.
Write in logarithmic form.
52 = 25
52 = 25
a)
log52 = 25
b)
log225 = 5
c)
log255 = 2
d)
log525 = 2
17.
Write in logarithmic form.
2-4 = 1/16
2-4 = 1/16
a)
log2(1/16) = -4
b)
log-4(1/16) = 2
c)
log -4 2 = 1/16
d)
log2(-4) = 1/16
18.
Evaluate the log:
log3(1/9) =
log3(1/9) =
a)
1/2
b)
2
c)
-2
d)
3
19.
The common logarithm has what base?
a)
10
b)
0
c)
e
d)
-e
20.
log (1/10) =
a)
-2
b)
-1
c)
1
d)
2
21.
Evaluate.
3 log24
3 log24
a)
3
b)
6
c)
2
d)
4
22.
Evaluate.
3 log82
3 log82
a)
1/3
b)
3
c)
1
d)
9
23.
Evaluate.
log6(1/216)
log6(1/216)
a)
3
b)
1/3
c)
-1/3
d)
-3
24.
What is the Vertical Asymptote?
a)
x=5
b)
x=0
c)
y=0
d)
x=1
25.
What are the transformations of this graph?
a)
Right 1 Up 5
b)
Right 1 Down 5
c)
Left 1 Up 5
d)
Left 1 Down 5
26.
Find the inverse of y=5x-8
a)
y=log5(x-8)
b)
y=log5(x+8)
c)
y=log8(x-5)
d)
y=log8(x+5)
27.
Logarithmic functions are the inverse of...
a)
Linear Functions
b)
Exponential Functions
c)
Quadratic Functions
d)
Polynomial Functions
28.
Which transformations describe the function
f(x) = −4log3(x − 2) + 5?
f(x) = −4log3(x − 2) + 5?
a)
reflection over x-axis, shift right 2, shift up 5
b)
reflection over x-axis, shift right 2, shift up 5, vertical stretch
c)
reflection over y-axis, shift left 2, shift up 5
d)
reflection over x-axis, shift right 2, shift up 5, vertical shrink
29.
In the general log function
y = a*logb(x-h)+k, what letter tells us if the function has stretched, compressed, or reflected?
y = a*logb(x-h)+k, what letter tells us if the function has stretched, compressed, or reflected?
a)
a
b)
b
c)
h
d)
k
30.
In the general log function
y = a*logb(x-h)+k, what letter tells us if the function has moved up or down?
y = a*logb(x-h)+k, what letter tells us if the function has moved up or down?
a)
a
b)
b
c)
h
d)
k
31.
Find the domain of y = log10(x+3)-1
a)
x<-3
b)
x>-3
c)
x<3
d)
x>3
32.
Evaluate:
log41
log41
a)
0
b)
1
c)
4
d)
DNE
33.
What is the asymptote of the graph?
a)
x=2
b)
y=-2
c)
y=0
d)
y=-1
34.
What is the horizontal asymptote and what transformations have taken place?
y = 2x+2 + 1
y = 2x+2 + 1
a)
y = 2
right 2, up 1
right 2, up 1
b)
y = 1
left 2, up 1
left 2, up 1
c)
y = 1
right 2, up 1
right 2, up 1
d)
y = 2
right 1, up 2
right 1, up 2
35.
What is the horizontal asymptote for the graph of
f(x)=-2(3)x+4-8 ?
f(x)=-2(3)x+4-8 ?
a)
y=8
b)
y=-8
c)
x=-8
d)
x=-4
36.
Which function is exponential?
a)
f(x)
b)
h(x)
c)
g(x)
37.
What is the domain and range of
f(x) = log 3 (x + 1)?
f(x) = log 3 (x + 1)?
a)
D: (− ∞, ∞) R: (−1, ∞)
b)
D: (− ∞, ∞) R: (1, ∞)
c)
D: (−1, ∞) R: (− ∞, ∞)
d)
D: (1, ∞) R: (− ∞, ∞)
38.
Evaluate the following logarithm:
log40.5
a)
-1/2
b)
-2
c)
2
d)
1/2
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