1st semester Flashcards
(130 cards)
1
Q
Domain of a function
A
The set of allowable inputs for a function.
2
Q
Range of a function
A
The set of outputs resulting from the allowable domain of a function.
3
Q
function
A
A dependence relationship where each input has exactly one output.
4
Q
vertical asymptote
A
This is formed when: As the input approaches a constant, the function’s outputs approach infinity or negative infinity.
5
Q
horizontal asymptote
A
This is formed when: As the input approaches infinity, the function’s outputs approach a constant.
6
Q
exponential function
A
This function has outputs that change by a constant percent (ratio, factor) as x changes by a constant difference.
7
Q
linear function
A
This function has a constant rate of change.
8
Q
horizontal line
A
This function is constant.
9
Q
concave up
A
The part of a graph where the rate of change is increasing.
10
Q
concave down
A
The part of a graph where the rate of change is decreasing.
11
Q
decreasing exponential function
A
An exponential function where the growth factor is between 0 and 1.
12
Q
increasing exponential function
A
An exponential function where the growth factor is greater than 1.
13
Q
average rate of change
A
The difference in the outputs divided by the difference in inputs over a given interval.
14
Q
Given f(x) = ax, find f(b)
A
ab
15
Q
Given f(x) = 3x + 2 + x, find f(2).
A
10
16
Q
Find the inverse of f(x) = 2x + 3
A
f’(x) = (x–3)/2
17
Q
If g(t) = n, what is g’(n)?
A
t
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.
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.
20
Q
If the growth rate of an exponential function is 3.4% per year, what is the growth factor?
A
1.034
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
22
Q
If the decrease rate of an exponential function is 9.2% per year, what is the growth factor?
A
0.908
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
24
Q
If the growth factor of an exponential function is 1.075, what is the growth rate?
A
7.5%
25
If the growth factor of an exponential function is 0.63, what is the decay rate?
37%
26
In the formula for an exponential function y = ab^x, what is a?
the y-intercept; the "initial" amount when t = 0.
27
Common logarithm
the power of 10 that produces a given number
28
Natural logarithm
the power of e that produces a given number
29
log 10
1
30
ln e
1
31
log 100,000
5
32
ln e^2
2
33
log(ab)
log(a) + log(b)
34
ln(a/b)
ln(a) – ln(b)
35
log(b)^t
t•log(b)
36
log(10^x)
x
37
10^(logx)
x
38
one order of magnitude larger
10 times larger
39
two orders of magnitude larger
100 times larger
40
three orders of magnitude larger
1000 times larger
41
Domain of y = log(x)
{reals \> 0}
42
Range of y = ln(x)
{all reals}
43
Domain of y = 2^x
{all reals}
44
Range of y = 2^x
{all reals \> 0}
45
f(x) + 3 produces what transformation on f(x)?
up three units
46
f(x – 5) produces what transformation on f(x)?
right five units
47
2f(x) produces what transformation on f(x)?
stretch vertically by a factor of 2 AWAY from the x-axis
48
f(3x) produces what transformation on f(x)?
compression TOWARD the y-axis by a factor of 1/3.
49
–f(x) produces what transformation on f(x)?
reflection over the x-axis
50
f(–x) produces what transformation on f(x)?
reflection over the y-axis
51
functions with y-axis symmetry
even functions
52
functions with origin symmetry
odd functions
53
y = 4/3x – 12
the equation for a linear function with slope 4/3 and y-intercept at (0, -12)
54
y = 320•(1.034)^t
the equation for an exponential function with initial amount 320 and growth rate of 3.4% per unit of time
55
two lines with the same rate of change (slope)
parallel lines
56
two lines whose slopes are opposite reciprocals
perpendicular lines
57
f(3) = 20
the symbolic representation of "function f at 3 is 20" OR "an input of 3 into function f has an output of 20"
58
h(t) = 300
the symbolic representation of "function h at t is 300" OR "an input of t into function g has an output of 300"
59
If a function approaches infinity as x approaches 3, then the function has this type of asymptote.
vertical asymptote
60
If a function approaches 4 as x approaches infinity, then the function has this type of asymptote.
horizontal asymptote
61
The equation of a parabola (in vertex form) with vertex (b, 4)
y = a(x – b)^2 +4
62
∆Q/∆x
the formula for average rate of change over a given interval
63
Write log(3x) = 4 in exponential form.
10^4 = 3x
64
Write 5x = 10^(4y) in logarithmic form.
log(5x) = 4y
65
Simplify: log(3 – 7y)
This log expression is already simplified. No log properties apply.
66
# (reverse question)
The set of allowable inputs for a function.
Domain of a function
67
# (reverse question)
The set of outputs resulting from the allowable domain of a function.
Range of a function
68
# (reverse question)
A dependence relationship where each input has exactly one output.
function
69
# (reverse question)
This is formed when: As the input approaches a constant, the function's outputs approach infinity or negative infinity.
vertical asymptote
70
# (reverse question)
This is formed when: As the input approaches infinity, the function's outputs approach a constant.
horizontal asymptote
71
# (reverse question)
This function has outputs that change by a constant percent (ratio, factor) as x changes by a constant difference.
exponential function
72
# (reverse question)
This function has a constant rate of change.
linear function
73
# (reverse question)
This function is constant.
horizontal line
74
# (reverse question)
The part of a graph where the rate of change is increasing.
concave up
75
# (reverse question)
The part of a graph where the rate of change is decreasing.
concave down
76
# (reverse question)
An exponential function where the growth factor is between 0 and 1.
decreasing exponential function
77
# (reverse question)
An exponential function where the growth factor is greater than 1.
increasing exponential function
78
# (reverse question)
The difference in the outputs divided by the difference in inputs over a given interval.
average rate of change
79
# (reverse question)
ab
Given f(x) = ax, find f(b)
80
# (reverse question)
10
Given f(x) = 3x + 2 + x, find f(2).
81
# (reverse question)
f'(x) = (x–3)/2
Find the inverse of f(x) = 2x + 3
82
# (reverse question)
t
If g(t) = n, what is g'(n)?
83
# (reverse question)
The height of the ball at 3 seconds is 10 feet.
If h(t) is the height in feet of a ball at time t in seconds, interpret h(3) = 10.
84
# (reverse question)
At 9 seconds, the the height of the ball is 8 feet.
If h(t) is the height in feet of a ball at time t in seconds, interpret h'(8) =9.
85
# (reverse question)
1.034
If the growth rate of an exponential function is 3.4% per year, what is the growth factor?
86
# (reverse question)
0.059
If the continuous growth rate of an exponential function is 5.9% per year, what is the "k" number in the formula?
87
# (reverse question)
0.908
If the decrease rate of an exponential function is 9.2% per year, what is the growth factor?
88
# (reverse question)
-0.0345
If the continuous decay rate of an exponential function is 3.45% per year, what is the "k" number in the formula?
89
# (reverse question)
7.5%
If the growth factor of an exponential function is 1.075, what is the growth rate?
90
# (reverse question)
37%
If the growth factor of an exponential function is 0.63, what is the decay rate?
91
# (reverse question)
the y-intercept; the "initial" amount when t = 0.
In the formula for an exponential function y = ab^x, what is a?
92
# (reverse question)
the power of 10 that produces a given number
Common logarithm
93
# (reverse question)
the power of e that produces a given number
Natural logarithm
94
# (reverse question)
1
log 10
95
# (reverse question)
1
ln e
96
# (reverse question)
5
log 100,000
97
# (reverse question)
2
ln e^2
98
# (reverse question)
log(a) + log(b)
log(ab)
99
# (reverse question)
ln(a) – ln(b)
ln(a/b)
100
# (reverse question)
t•log(b)
log(b)^t
101
# (reverse question)
x
log(10^x)
102
# (reverse question)
x
10^(logx)
103
# (reverse question)
10 times larger
one order of magnitude larger
104
# (reverse question)
100 times larger
two orders of magnitude larger
105
# (reverse question)
1000 times larger
three orders of magnitude larger
106
# (reverse question)
{reals \> 0}
Domain of y = log(x)
107
# (reverse question)
{all reals}
Range of y = ln(x)
108
# (reverse question)
{all reals}
Domain of y = 2^x
109
# (reverse question)
{all reals \> 0}
Range of y = 2^x
110
# (reverse question)
up three units
f(x) + 3 produces what transformation on f(x)?
111
# (reverse question)
right five units
f(x – 5) produces what transformation on f(x)?
112
# (reverse question)
stretch vertically by a factor of 2 AWAY from the x-axis
2f(x) produces what transformation on f(x)?
113
# (reverse question)
compression TOWARD the y-axis by a factor of 1/3.
f(3x) produces what transformation on f(x)?
114
# (reverse question)
reflection over the x-axis
–f(x) produces what transformation on f(x)?
115
# (reverse question)
reflection over the y-axis
f(–x) produces what transformation on f(x)?
116
# (reverse question)
even functions
functions with y-axis symmetry
117
# (reverse question)
odd functions
functions with origin symmetry
118
# (reverse question)
the equation for a linear function with slope 4/3 and y-intercept at (0, -12)
y = 4/3x – 12
119
# (reverse question)
the equation for an exponential function with initial amount 320 and growth rate of 3.4% per unit of time
y = 320•(1.034)^t
120
# (reverse question)
parallel lines
two lines with the same rate of change (slope)
121
# (reverse question)
perpendicular lines
two lines whose slopes are opposite reciprocals
122
# (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"
f(3) = 20
123
# (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"
h(t) = 300
124
# (reverse question)
vertical asymptote
If a function approaches infinity as x approaches 3, then the function has this type of asymptote.
125
# (reverse question)
horizontal asymptote
If a function approaches 4 as x approaches infinity, then the function has this type of asymptote.
126
# (reverse question)
y = a(x – b)^2 +4
The equation of a parabola (in vertex form) with vertex (b, 4)
127
# (reverse question)
the formula for average rate of change over a given interval
∆Q/∆x
128
# (reverse question)
10^4 = 3x
Write log(3x) = 4 in exponential form.
129
# (reverse question)
log(5x) = 4y
Write 5x = 10^(4y) in logarithmic form.
130
# (reverse question)
This log expression is already simplified. No log properties apply.
Simplify: log(3 – 7y)
