Spring 2022 Flashcards
1
Q
What is the system’s term for Precalculus?
A
MATH 126
2
Q
Who is your professor?
A
Mr. Zachary Sperling
3
Q
What is Professor Sperling’s email?
A
SPERLINZ@star.lcc.edu
4
Q
Where is Professor Sperling’s office?
A
In the Arts and Sciences (A&S) Building, Room 3203 Arts and Sciences
5
Q
What is the Science and Mathematics Department Phone Number?
A
517-483-1073
6
Q
cm
A
centimeter
7
Q
dB
A
decibel
8
Q
F
A
farad
9
Q
ft
A
foot
10
Q
g
A
gram
11
Q
gal
A
gallon
12
Q
H
A
Henry
13
Q
Hz
A
Hertz
14
Q
in.
A
inch
15
Q
J
A
Joule
16
Q
kcal
A
kilocalorie
17
Q
kg
A
kilogram
18
Q
km
A
kilometer
19
Q
kPa
A
kilopascal
20
Q
L
A
Liter
21
Q
lb
A
pound
22
Q
lm
A
Lumen
23
Q
M
A
Mole of solute per liter of solution
24
Q
m
A
meter
25
mg
milligram
26
MHz
megahertz
27
mi
mile
28
min
minute
29
mL
milliliter
30
mm
millimeter
31
N
Newton
32
qt
quart
33
oz
ounce
34
s
seconds
35
Ω
ohm
36
V
volt
37
W
watt
38
yd
yard
39
yr
year
40
°C
degrees Celsius
41
°F
degrees Fahrenheit
42
K
Kelvin
43
→
implies
44
↔
is equivalent to
45
D (density) =
M (mass) / V (volume)
46
crux
the decisive or most important point at issue
47
Natural Numbers
1, 2, 3, 4, 5, ...
48
Whole Numbers
0, 1, 2, 3, 4, ...
49
Integers
..., -2, -1, 0, 1, 2, ...
50
Rational Numbers
..., -1, 0, 0.5, 3/4, 1, ...
51
Irrational Numbers
sqrt. {2}, pi, ...
52
Real Numbers
((Irrational Numbers)(Rational Numbers(Integers(Whole Numbers(Natural Numbers)))))
53
Imaginary Numbers
i = sqrt. {-1}, 3+5i, etc.
54
Complex Numbers
((Real Numbers)(Imaginary Numbers))
55
denote
be a sign of; indicate
56
Property of Exponents
| a^m)(a^n
= a^{m+n}
57
Property of Exponents
| (a^m)^n
= a^{m*n}
58
Property of Exponents
| (ab)^n
= (a^n)(b^n)
59
Property of Exponents
| a^{-n}
= 1/a^n*
| *unless a = 0
60
Property of Exponents
| (a/b)^n
= (a^n)/(b^n)
61
Property of Exponents
| (a/b)^{-n}
= (b/a)^n
62
Property of Exponents
| a^0
= 1*
| *unless a = 0
63
Property of Exponents
| a^m)/(a^n
a^{m-n}
64
Linear Function
y = x
65
Quadratic Funtion
y = x^2
66
Square Root Function
y = \sqrt. {x}
67
Absolute Value Function
y = |x|
68
Regarding function transformations: Vetical Shifting
Suppose c > 0.
To graph y = f(x) + c, shift the graph of y = f(x) upward c units.
To graph y = f(x) - c, shift the graph og y = f(x) downward c units.
69
Regarding function transformations: Horizontal Shifting
Suppose c > 0
To graph y = f(x - c), shift the graph of y = f(x) to the right c units.
To graph y = f(x + c), shift the graph of y = f(x) to the left c units.
70
Regarding function transformations: Refelcting Graphs
To graph y = -f(x), reflect the graph of y = f(x) in the x-axis.
To graph y = f(-x), reflect the graph of y = f(x) in the y-axis.
Reflecting about the x-axis:
y = f(x) ; above the x-axis
y = - f(x) ; below the x-axis
Refecting about he y-axis:
y = f(x) ; to the right of the y-axis
y = f(-x) ; to the left of the y-axis
71
Regarding function transformations: Vertical Stretching and Shrinking
On a graph, y = (c)(f(x))
If c > 1, the graph of y = f(x) is vertically stretched by a factor of c ; pull the function up and down at the same time with the same force.
If c < 1, the graph of y = f(x) vertically shrinks by a factor of c ; squeeze the function from above and below at the same time with the same force.
72
Regarding function transformations: Horizontal Stretching and Shrinking
On a graph, y = f(x/c)
If c > 1, shrink the graph of y = f(x) horizontally by a factor of 1/c.
If 0 < c < 1, stretch the graph of y = f(x) horrizontally by a factor of 1/c.
73
What's an even function?
A function when the opposite inputs give the same outputs (x or -x -> y) ; horrizontally symmetric.
f(-x) = f(x)
e.g. f(-x) = (-x)^2 = x^2
74
What is an odd function?
A function when opposite inputs give opposite outputs ( f(-x) = -f(x) ) ; not symmetric about the y-axis, but symmetric about the origin.
e.g. f(x) = x^3
75
Are functions only either odd or even?
Functions can be odd, even, or neither, so no.
76
What does the Horizontal Line Test say about a function?
A function is one-to-one if only and only if no horoizontal line intersects its graph more than once.
I.e. the Horizontal Line test determines weather a fuction is one-to-one or not.
77
2.8 One-to-One Functions and Their Inverses
What is the Definition of A One-to-One Function?
A one to one function is a function with Domain A is no two elements of A have the same image, that is,
f(x_1) =/= f(x_2) when (x_1)/(x_2)
78
2.8 One-to-One Functions and Their Inverses
What is the Horizontal Line Test?
The horizontal line test determines a function being one-to-one if and only if no horizontal line intersects its graph more than once.
79
2.8 One-to-One Functions and Their Inverses
Wht is the Definition of the Inverse of a Function?
Let f be a one-to-one function with Domain A and Range B. Then its inverse function F^(-1) has Domain B and Range A, and is defined by
f^(-1)(y) = x f(x) = y
for any y in B.
80
2.8 One-to-One Functions and Their Inverses
What is Inverse Function Property?
Let f be a one-to-one function with Domain A and Range B. The inverse function f^(-1) satisfies the following cancellation properties:
f^(-1)(f(x)) = x for every x in A
f(f^(-1)(x)) = x for every x in B
Conversely, any function f^(-1) satisfying these equations is the inverse of f.
