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Precalculus > Spring 2022 > Flashcards

Spring 2022 Flashcards

1
Q

What is the system’s term for Precalculus?

A

MATH 126

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2
Q

Who is your professor?

A

Mr. Zachary Sperling

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3
Q

What is Professor Sperling’s email?

A

SPERLINZ@star.lcc.edu

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4
Q

Where is Professor Sperling’s office?

A

In the Arts and Sciences (A&S) Building, Room 3203 Arts and Sciences

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5
Q

What is the Science and Mathematics Department Phone Number?

A

517-483-1073

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6
Q

cm

A

centimeter

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7
Q

dB

A

decibel

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8
Q

F

A

farad

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9
Q

ft

A

foot

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10
Q

g

A

gram

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11
Q

gal

A

gallon

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12
Q

H

A

Henry

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13
Q

Hz

A

Hertz

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14
Q

in.

A

inch

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15
Q

J

A

Joule

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16
Q

kcal

A

kilocalorie

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17
Q

kg

A

kilogram

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18
Q

km

A

kilometer

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19
Q

kPa

A

kilopascal

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20
Q

L

A

Liter

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21
Q

lb

A

pound

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22
Q

lm

A

Lumen

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23
Q

M

A

Mole of solute per liter of solution

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24
Q

m

A

meter

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25
Q

mg

A

milligram

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26
Q

MHz

A

megahertz

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27
Q

mi

A

mile

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28
Q

min

A

minute

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29
Q

mL

A

milliliter

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30
Q

mm

A

millimeter

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31
Q

N

A

Newton

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32
Q

qt

A

quart

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33
Q

oz

A

ounce

34
Q

s

A

seconds

35
Q

Ω

A

ohm

36
Q

V

A

volt

37
Q

W

A

watt

38
Q

yd

A

yard

39
Q

yr

A

year

40
Q

°C

A

degrees Celsius

41
Q

°F

A

degrees Fahrenheit

42
Q

K

A

Kelvin

43
Q

→

A

implies

44
Q

↔

A

is equivalent to

45
Q

D (density) =

A

M (mass) / V (volume)

46
Q

crux

A

the decisive or most important point at issue

47
Q

Natural Numbers

A

1, 2, 3, 4, 5, …

48
Q

Whole Numbers

A

0, 1, 2, 3, 4, …

49
Q

Integers

A

…, -2, -1, 0, 1, 2, …

50
Q

Rational Numbers

A

…, -1, 0, 0.5, 3/4, 1, …

51
Q

Irrational Numbers

A

sqrt. {2}, pi, …

52
Q

Real Numbers

A

((Irrational Numbers)(Rational Numbers(Integers(Whole Numbers(Natural Numbers)))))

53
Q

Imaginary Numbers

A

i = sqrt. {-1}, 3+5i, etc.

54
Q

Complex Numbers

A

((Real Numbers)(Imaginary Numbers))

55
Q

denote

A

be a sign of; indicate

56
Q

Property of Exponents

a^m)(a^n

A

= a^{m+n}

57
Q

Property of Exponents

(a^m)^n

A

= a^{m*n}

58
Q

Property of Exponents

(ab)^n

A

= (a^n)(b^n)

59
Q

Property of Exponents

a^{-n}

A

= 1/a^n*

*unless a = 0

60
Q

Property of Exponents

(a/b)^n

A

= (a^n)/(b^n)

61
Q

Property of Exponents

(a/b)^{-n}

A

= (b/a)^n

62
Q

Property of Exponents

a^0

A

= 1*

*unless a = 0

63
Q

Property of Exponents

a^m)/(a^n

A

a^{m-n}

64
Q

Linear Function

A

y = x

65
Q

Quadratic Funtion

A

y = x^2

66
Q

Square Root Function

A

y = \sqrt. {x}

67
Q

Absolute Value Function

A

y = |x|

68
Q

Regarding function transformations: Vetical Shifting

A

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
Q

Regarding function transformations: Horizontal Shifting

A

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
Q

Regarding function transformations: Refelcting Graphs

A

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
Q

Regarding function transformations: Vertical Stretching and Shrinking

A

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
Q

Regarding function transformations: Horizontal Stretching and Shrinking

A

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
Q

What’s an even function?

A

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
Q

What is an odd function?

A

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
Q

Are functions only either odd or even?

A

Functions can be odd, even, or neither, so no.

76
Q

What does the Horizontal Line Test say about a function?

A

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
Q

2.8 One-to-One Functions and Their Inverses

What is the Definition of A One-to-One Function?

A

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
Q

2.8 One-to-One Functions and Their Inverses

What is the Horizontal Line Test?

A

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
Q

2.8 One-to-One Functions and Their Inverses

Wht is the Definition of the Inverse of a Function?

A

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
Q

2.8 One-to-One Functions and Their Inverses

What is Inverse Function Property?

A

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.

Precalculus (1 decks)

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