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Precalculus > 1st semester > Flashcards

1st semester Flashcards

1
Q

Domain of a function

A

The set of allowable inputs for a function.

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2
Q

Range of a function

A

The set of outputs resulting from the allowable domain of a function.

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3
Q

function

A

A dependence relationship where each input has exactly one output.

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4
Q

vertical asymptote

A

This is formed when: As the input approaches a constant, the function’s outputs approach infinity or negative infinity.

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5
Q

horizontal asymptote

A

This is formed when: As the input approaches infinity, the function’s outputs approach a constant.

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6
Q

exponential function

A

This function has outputs that change by a constant percent (ratio, factor) as x changes by a constant difference.

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7
Q

linear function

A

This function has a constant rate of change.

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8
Q

horizontal line

A

This function is constant.

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9
Q

concave up

A

The part of a graph where the rate of change is increasing.

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10
Q

concave down

A

The part of a graph where the rate of change is decreasing.

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11
Q

decreasing exponential function

A

An exponential function where the growth factor is between 0 and 1.

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12
Q

increasing exponential function

A

An exponential function where the growth factor is greater than 1.

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13
Q

average rate of change

A

The difference in the outputs divided by the difference in inputs over a given interval.

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14
Q

Given f(x) = ax, find f(b)

A

ab

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15
Q

Given f(x) = 3x + 2 + x, find f(2).

A

10

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16
Q

Find the inverse of f(x) = 2x + 3

A

f’(x) = (x–3)/2

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17
Q

If g(t) = n, what is g’(n)?

A

t

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18
Q

If h(t) is the height in feet of a ball at time t in seconds, interpret h(3) = 10.

A

The height of the ball at 3 seconds is 10 feet.

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19
Q

If h(t) is the height in feet of a ball at time t in seconds, interpret h’(8) =9.

A

At 9 seconds, the the height of the ball is 8 feet.

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20
Q

If the growth rate of an exponential function is 3.4% per year, what is the growth factor?

A

1.034

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21
Q

If the continuous growth rate of an exponential function is 5.9% per year, what is the “k” number in the formula?

A

0.059

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22
Q

If the decrease rate of an exponential function is 9.2% per year, what is the growth factor?

A

0.908

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23
Q

If the continuous decay rate of an exponential function is 3.45% per year, what is the “k” number in the formula?

A

-0.0345

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24
Q

If the growth factor of an exponential function is 1.075, what is the growth rate?

A

7.5%

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25
Q

If the growth factor of an exponential function is 0.63, what is the decay rate?

A

37%

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26
Q

In the formula for an exponential function y = ab^x, what is a?

A

the y-intercept; the “initial” amount when t = 0.

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27
Q

Common logarithm

A

the power of 10 that produces a given number

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28
Q

Natural logarithm

A

the power of e that produces a given number

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29
Q

log 10

A

1

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30
Q

ln e

A

1

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31
Q

log 100,000

A

5

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32
Q

ln e^2

A

2

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33
Q

log(ab)

A

log(a) + log(b)

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34
Q

ln(a/b)

A

ln(a) – ln(b)

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35
Q

log(b)^t

A

t•log(b)

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36
Q

log(10^x)

A

x

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37
Q

10^(logx)

A

x

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38
Q

one order of magnitude larger

A

10 times larger

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39
Q

two orders of magnitude larger

A

100 times larger

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40
Q

three orders of magnitude larger

A

1000 times larger

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41
Q

Domain of y = log(x)

A

{reals > 0}

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42
Q

Range of y = ln(x)

A

{all reals}

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43
Q

Domain of y = 2^x

A

{all reals}

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44
Q

Range of y = 2^x

A

{all reals > 0}

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45
Q

f(x) + 3 produces what transformation on f(x)?

A

up three units

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46
Q

f(x – 5) produces what transformation on f(x)?

A

right five units

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47
Q

2f(x) produces what transformation on f(x)?

A

stretch vertically by a factor of 2 AWAY from the x-axis

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48
Q

f(3x) produces what transformation on f(x)?

A

compression TOWARD the y-axis by a factor of 1/3.

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49
Q

–f(x) produces what transformation on f(x)?

A

reflection over the x-axis

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50
Q

f(–x) produces what transformation on f(x)?

A

reflection over the y-axis

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51
Q

functions with y-axis symmetry

A

even functions

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52
Q

functions with origin symmetry

A

odd functions

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53
Q

y = 4/3x – 12

A

the equation for a linear function with slope 4/3 and y-intercept at (0, -12)

54
Q

y = 320•(1.034)^t

A

the equation for an exponential function with initial amount 320 and growth rate of 3.4% per unit of time

55
Q

two lines with the same rate of change (slope)

A

parallel lines

56
Q

two lines whose slopes are opposite reciprocals

A

perpendicular lines

57
Q

f(3) = 20

A

the symbolic representation of “function f at 3 is 20” OR “an input of 3 into function f has an output of 20”

58
Q

h(t) = 300

A

the symbolic representation of “function h at t is 300” OR “an input of t into function g has an output of 300”

59
Q

If a function approaches infinity as x approaches 3, then the function has this type of asymptote.

A

vertical asymptote

60
Q

If a function approaches 4 as x approaches infinity, then the function has this type of asymptote.

A

horizontal asymptote

61
Q

The equation of a parabola (in vertex form) with vertex (b, 4)

A

y = a(x – b)^2 +4

62
Q

∆Q/∆x

A

the formula for average rate of change over a given interval

63
Q

Write log(3x) = 4 in exponential form.

A

10^4 = 3x

64
Q

Write 5x = 10^(4y) in logarithmic form.

A

log(5x) = 4y

65
Q

Simplify: log(3 – 7y)

A

This log expression is already simplified. No log properties apply.

66
Q

(reverse question)

The set of allowable inputs for a function.

A

Domain of a function

67
Q

(reverse question)

The set of outputs resulting from the allowable domain of a function.

A

Range of a function

68
Q

(reverse question)

A dependence relationship where each input has exactly one output.

A

function

69
Q

(reverse question)

This is formed when: As the input approaches a constant, the function’s outputs approach infinity or negative infinity.

A

vertical asymptote

70
Q

(reverse question)

This is formed when: As the input approaches infinity, the function’s outputs approach a constant.

A

horizontal asymptote

71
Q

(reverse question)

This function has outputs that change by a constant percent (ratio, factor) as x changes by a constant difference.

A

exponential function

72
Q

(reverse question)

This function has a constant rate of change.

A

linear function

73
Q

(reverse question)

This function is constant.

A

horizontal line

74
Q

(reverse question)

The part of a graph where the rate of change is increasing.

A

concave up

75
Q

(reverse question)

The part of a graph where the rate of change is decreasing.

A

concave down

76
Q

(reverse question)

An exponential function where the growth factor is between 0 and 1.

A

decreasing exponential function

77
Q

(reverse question)

An exponential function where the growth factor is greater than 1.

A

increasing exponential function

78
Q

(reverse question)

The difference in the outputs divided by the difference in inputs over a given interval.

A

average rate of change

79
Q

(reverse question)

ab

A

Given f(x) = ax, find f(b)

80
Q

(reverse question)

10

A

Given f(x) = 3x + 2 + x, find f(2).

81
Q

(reverse question)

f’(x) = (x–3)/2

A

Find the inverse of f(x) = 2x + 3

82
Q

(reverse question)

t

A

If g(t) = n, what is g’(n)?

83
Q

(reverse question)

The height of the ball at 3 seconds is 10 feet.

A

If h(t) is the height in feet of a ball at time t in seconds, interpret h(3) = 10.

84
Q

(reverse question)

At 9 seconds, the the height of the ball is 8 feet.

A

If h(t) is the height in feet of a ball at time t in seconds, interpret h’(8) =9.

85
Q

(reverse question)

1.034

A

If the growth rate of an exponential function is 3.4% per year, what is the growth factor?

86
Q

(reverse question)

0.059

A

If the continuous growth rate of an exponential function is 5.9% per year, what is the “k” number in the formula?

87
Q

(reverse question)

0.908

A

If the decrease rate of an exponential function is 9.2% per year, what is the growth factor?

88
Q

(reverse question)

-0.0345

A

If the continuous decay rate of an exponential function is 3.45% per year, what is the “k” number in the formula?

89
Q

(reverse question)

7.5%

A

If the growth factor of an exponential function is 1.075, what is the growth rate?

90
Q

(reverse question)

37%

A

If the growth factor of an exponential function is 0.63, what is the decay rate?

91
Q

(reverse question)

the y-intercept; the “initial” amount when t = 0.

A

In the formula for an exponential function y = ab^x, what is a?

92
Q

(reverse question)

the power of 10 that produces a given number

A

Common logarithm

93
Q

(reverse question)

the power of e that produces a given number

A

Natural logarithm

94
Q

(reverse question)

1

A

log 10

95
Q

(reverse question)

1

A

ln e

96
Q

(reverse question)

5

A

log 100,000

97
Q

(reverse question)

2

A

ln e^2

98
Q

(reverse question)

log(a) + log(b)

A

log(ab)

99
Q

(reverse question)

ln(a) – ln(b)

A

ln(a/b)

100
Q

(reverse question)

t•log(b)

A

log(b)^t

101
Q

(reverse question)

x

A

log(10^x)

102
Q

(reverse question)

x

A

10^(logx)

103
Q

(reverse question)

10 times larger

A

one order of magnitude larger

104
Q

(reverse question)

100 times larger

A

two orders of magnitude larger

105
Q

(reverse question)

1000 times larger

A

three orders of magnitude larger

106
Q

(reverse question)

{reals > 0}

A

Domain of y = log(x)

107
Q

(reverse question)

{all reals}

A

Range of y = ln(x)

108
Q

(reverse question)

{all reals}

A

Domain of y = 2^x

109
Q

(reverse question)

{all reals > 0}

A

Range of y = 2^x

110
Q

(reverse question)

up three units

A

f(x) + 3 produces what transformation on f(x)?

111
Q

(reverse question)

right five units

A

f(x – 5) produces what transformation on f(x)?

112
Q

(reverse question)

stretch vertically by a factor of 2 AWAY from the x-axis

A

2f(x) produces what transformation on f(x)?

113
Q

(reverse question)

compression TOWARD the y-axis by a factor of 1/3.

A

f(3x) produces what transformation on f(x)?

114
Q

(reverse question)

reflection over the x-axis

A

–f(x) produces what transformation on f(x)?

115
Q

(reverse question)

reflection over the y-axis

A

f(–x) produces what transformation on f(x)?

116
Q

(reverse question)

even functions

A

functions with y-axis symmetry

117
Q

(reverse question)

odd functions

A

functions with origin symmetry

118
Q

(reverse question)

the equation for a linear function with slope 4/3 and y-intercept at (0, -12)

A

y = 4/3x – 12

119
Q

(reverse question)

the equation for an exponential function with initial amount 320 and growth rate of 3.4% per unit of time

A

y = 320•(1.034)^t

120
Q

(reverse question)

parallel lines

A

two lines with the same rate of change (slope)

121
Q

(reverse question)

perpendicular lines

A

two lines whose slopes are opposite reciprocals

122
Q

(reverse question)

the symbolic representation of “function f at 3 is 20” OR “an input of 3 into function f has an output of 20”

A

f(3) = 20

123
Q

(reverse question)

the symbolic representation of “function h at t is 300” OR “an input of t into function g has an output of 300”

A

h(t) = 300

124
Q

(reverse question)

vertical asymptote

A

If a function approaches infinity as x approaches 3, then the function has this type of asymptote.

125
Q

(reverse question)

horizontal asymptote

A

If a function approaches 4 as x approaches infinity, then the function has this type of asymptote.

126
Q

(reverse question)

y = a(x – b)^2 +4

A

The equation of a parabola (in vertex form) with vertex (b, 4)

127
Q

(reverse question)

the formula for average rate of change over a given interval

A

∆Q/∆x

128
Q

(reverse question)

10^4 = 3x

A

Write log(3x) = 4 in exponential form.

129
Q

(reverse question)

log(5x) = 4y

A

Write 5x = 10^(4y) in logarithmic form.

130
Q

(reverse question)

This log expression is already simplified. No log properties apply.

A

Simplify: log(3 – 7y)

Precalculus (3 decks)

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