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College Algebra > 4.1-4.4 Vocabulary/Formulas/Rules > Flashcards

4.1-4.4 Vocabulary/Formulas/Rules Flashcards

Logarithms and Exponential Functions

1
Q

functions that involve some combination of basic arithmetic operations, powers, or roots

A

algebraic functions

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2
Q

functions used to describe phenomena from growth of investments to decay of radioactive material such as exponential and logarithmic functions

A

transcendental functions

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3
Q

Give examples of algebraic functions

A
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4
Q

What is the equation of an exponential function?

A
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5
Q

What is the domain for an exponential function?

A
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6
Q

With the function below, is the function increasing or decreasing? Explain.

A

Increasing, the base of 2 is greater than 1.

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7
Q

With the function below, is the function increasing or decreasing? Explain.

A

Decreasing, the base of 1/2 is between 0 and 1.

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8
Q

What could change a exponential function from increasing to decreasing?

A

a reflection in the x or y axis

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9
Q

What must be included with every exponential graph?

A

table, 3 points and a horizontal asymptote

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10
Q

In the following equation, what does “b” stand for?

A

If b>1, vertical stretch.
if 0<b<1, vertical shrink
if b<0, reflection over the x-axis.

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11
Q

In the following equation what does the “a” stand for?

A

The base of the exponential function.
The base will determine if the “parent” graph increases or decreases
If a>1, the graph increases originally.
If 0<a<1, the graph decreases originally.
“a” can never be negative.

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12
Q

In the following equation what does the “c” stand for?

A

If c > 1, horizontal compression by the reciprocal.
If 0 < c < 1, horizontal stretch by the reciprocal.
If c < 0, y-axis reflection.

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13
Q

In the following equation what does the “cx-h” stand for?

A

Set cx-h = 0 and solve for x. This will determine your horizontal translation.

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14
Q

In the following equation what does the “k” stand for?

A

vertical translation

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15
Q

What transformation changes the location of the horizontal asymptote in exponential graphs?

A

vertical translation

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16
Q

What transformation changes the range of the exponential graphs?

A

vertical translation

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17
Q

Without a vertical translation, what is the range of the exponential function?

A
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18
Q

State the one-to-one property for exponential functions

A
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19
Q

What is the first way you should try to solve exponential equations?

A

Try to see if you can make the bases on both sides of the equation the same base. Then use the one-to-one property.

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20
Q

What is the natural exponential function?

A
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21
Q

What is the domain of the natural exponential function?

A
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22
Q

What is the range of the natural exponential function (without transformations)?

A
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23
Q

Does the natural exponential function increase of decrease? Explain.

A

increase since “e” > 1

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24
Q

What is the approximation associated with the number “e”

A
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25
Q

A logarithm is the __________ of an exponential function

A

inverse

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26
Q

What is a logarithm?

A

an exponent from the base of an exponential function

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27
Q

What is a common logarithm?

A

logarithm with base 10

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28
Q

What is a natural logarithm

A

logarithm with base e

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29
Q

What is the logarithm of a negative number

A

undefined

30
Q

what is the logarithm of 0

A

undefined

31
Q

What is the domain of a logarithm graph without transformations?

A
32
Q

What is the range of a logarithmic graph without transformations?

A
33
Q

In the following equation, what does the “a” stand for?

A

It is the base. It determines whether the logarithm increases or decreases before transformations. If a > 1, the logarithm increases. If 0<a<1, then the logarithms decreases. The base can never be negative.

34
Q

In the following equation, what does the “b” stand for?

A

b>1 Vertical stretch
0<b<1 Vertical shrink
b<0 Reflection over the x-axis

35
Q

In the following equation, what does the “c” stand for?

A

c>1 Horizontal shrink by the reciprocal
0<c<1 Horizontal stretch by the reciprocal
c<0 Reflection over the y-axis

36
Q

In the following equation, what does the “cx-h” stand for?

A

If cx-h = 0 and solved for x, this will determine the horizontal translation. If positive, it goes right. If negative, it goes left.

37
Q

In the following equation, what does the k stand for?

A

Vertical translation

38
Q

What is the one-to-one property of logarithms?

A
39
Q

Graph the parent function of

A

don’t forget the asymptote

40
Q

Graph the parent function of

A

don’t forget the asymptote

41
Q

Graph the parent function of

A

don’t forget the asymptote

42
Q

Graph the parent function of

A

don’t forget the asymptote

43
Q

Graph the parent function of

A

don’t forget the asymptote

44
Q

Graph the parent function of

A

don’t forget the asymptote

45
Q

What must appear on every graphing problem?

A

Table

46
Q
A
47
Q
A
48
Q
A
49
Q
A
50
Q

What is the Product Rule for Exponentials?

A
51
Q

What is the Quotient Rule for Exponentials?

A
52
Q

What is the Power Rule for Exponentials?

A
53
Q

What is the zero exponent rule for exponentials?

A
54
Q

What is the Product Rule for Logarithms?

A
55
Q

What is the Quotient Rule for Logarithms?

A
56
Q

What is the Power Rule for Logarithms?

A
57
Q

What is the Zero Exponent rule for Logarithms?

A
58
Q

What is the Change-of-Base Formula?

A
59
Q
A

1

60
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61
Q
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1

62
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63
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64
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65
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66
Q
A

0

67
Q
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68
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69
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70
Q
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0

College Algebra (17 decks)

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