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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 (70 cards)

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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
A logarithm is the __________ of an exponential function
inverse
26
What is a logarithm?
an exponent from the base of an exponential function
27
What is a common logarithm?
logarithm with base 10
28
What is a natural logarithm
logarithm with base e
29
What is the logarithm of a negative number
undefined
30
what is the logarithm of 0
undefined
31
What is the domain of a logarithm graph without transformations?
32
What is the range of a logarithmic graph without transformations?
33
In the following equation, what does the "a" stand for?
It is the base. It determines whether the logarithm increases or decreases before transformations. If a > 1, the logarithm increases. If 0
34
In the following equation, what does the "b" stand for?
b>1 Vertical stretch 0
35
In the following equation, what does the "c" stand for?
c>1 Horizontal shrink by the reciprocal 0
36
In the following equation, what does the "cx-h" stand for?
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
In the following equation, what does the k stand for?
Vertical translation
38
What is the one-to-one property of logarithms?
39
Graph the parent function of
don't forget the asymptote
40
Graph the parent function of
don't forget the asymptote
41
Graph the parent function of
don't forget the asymptote
42
Graph the parent function of
don't forget the asymptote
43
Graph the parent function of
don't forget the asymptote
44
Graph the parent function of
don't forget the asymptote
45
What must appear on every graphing problem?
Table
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What is the Product Rule for Exponentials?
51
What is the Quotient Rule for Exponentials?
52
What is the Power Rule for Exponentials?
53
What is the zero exponent rule for exponentials?
54
What is the Product Rule for Logarithms?
55
What is the Quotient Rule for Logarithms?
56
What is the Power Rule for Logarithms?
57
What is the Zero Exponent rule for Logarithms?
58
What is the Change-of-Base Formula?
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College Algebra (17 decks)

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