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Flashcards in Calc from IFlipr Deck (75):
1

y= f(x) + 2, shifts the graph of y=f(x) a distance of 2 in a(n) _____ direction

upward

2

y= f(x) - 2, shifts the graph of y=f(x) a distance of 2 in a(n) _____ direction

downward

3

y= f(x + 2), shifts the graph of y=f(x) a distance of 2 in a(n) _____ direction

left

4

y= f(x - 2), shifts the graph of y=f(x) a distance of 2 in a(n) _____ direction

right

5

y= -f(x), does ____ in changes the graph of y=f(x)

reflects across the x-axis

6

y= f(-x), does ____ in changes the graph of y=f(x)

reflects across the y-axis

7

Sin(x) is equal to zero at which values of x

0, pi, 2pi...

8

F(x)= a^x is/is not One-to-One

is

9

The inverse of f(x)= a^x is ____

the logarithm

10

Log a (x) is the number that a" must be raised to in order to produce __"

x

11

log 10 (100)= ___, log 3 (1/81)= ___,log 4 (16) = ____

2;-4;2

12

A logarithm with base e" is called the ________ denoted ___"

natural logarithm; ln x

13

The natural logarithm of e equals ____ln e = ____

1, becuase e^1= e

14

Properties of Log: log a (xy) can also be written as _____

log a (x) + log a (y)

15

Properties of Log: log a (x/y) can also be written as ____

log a (x) - log a (y)

16

Properties of Log: log a (x^n) can also be written as ____

n log a (x)

17

Properties of Log: Any log can be expressed in terms of ln by the equation log a (x) = ____

ln(x)/ ln(a)

18

Trig: 180 degress is equal to ___ radians

pi

19

Trig: 1 degree is equal to ____ radians

pi/180

20

Trig: Zero degrees is equal to ____ radians

zero

21

Trig: 30 degrees is equal to ____ radians

pi/6

22

Trig: 60 degrees is equal to ____ radians

pi/3

23

Trig: 45 degrees is equal to ____ radians

pi/4

24

Trig: 90 degrees is equal to ____ radians

pi/2

25

Trig: sin theta = _ /_

y/r

26

Trig: cos theta = _ /_

x/r

27

Trig: tan theta = _ /_

y/x

28

Trig: cse theta = _ /_ or the opposite of ___

r/y; sin

29

Trig: sec theta = _ /_ or the opposite of ____

r/x; cos

30

Trig: cot theta = _ /_ or the opposite of ___

x/y; tan

31

Trig: sin (0) = ___

0

32

Trig: sin (π/6) = ___

2-Jan

33

Trig: sin (π/4) = ____

√2/2

34

Trig: sin (π/3) = ____

√3/2

35

Trig: sin(π/2)= ___

1

36

Trig: sin(π)= ___

o

37

Trig: sin(3π/2)= ___

-1

38

Trig: sin(2π)= ___

0

39

Trig: cos(0)= ___

1

40

Trig: cos(π/6)= ___

√3/2

41

Trig: cos(π/4)= ____

√2/2

42

Trig: cos(π/3)= ___

2-Jan

43

Trig: cos(π/2)= ___

0

44

Trig: cos(π)= ___

-1

45

Trig: cos(3π/2)= ____

0

46

Trig: cos(2π)= ____

1

47

Trig Rules: tan theta =

sin theta/ cos theta

48

Trig Rules: sin^2 theta + cos ^2 theta=

1

49

Trig Rules: sin(- theta)=

#NAME?

50

Trig Rules: cos (- theta)=

cos theta

51

Trig Rules: sin (theta + 2π)=

sin theta

52

Trig Rules:  sin(x+y)=

sin(x)cos(y) + cos(x)sin(y)

53

Trig Rules: cos(x+y)=

cos(x)cos(y) + sin(x)sin(y)

54

Theorm that states if f(x)=g(x) for x's that do not equal a, then the limit of f(x) as x approaches a is equal to the limit of g(x) as x approaches a

Alternate Function Theorm

55

With every ____ and ____ function the limit as x approaches a can is no different than defining the equation with x=a (ex. lim as x approaches 3 of x^2+2x+4 is the same as x=3 x^2+2x+4)

polynomial; rational

56

A function is continuous at the number a if small changes in x values result in small changes in _____

function values

57

If function f is continuous from a until b with both of those point being included, than domain is ____

continuous from [a,b]

58

If function f is continuous from a until b with both of those point not being included, than domain is ____

continuous from (a,b)

59

If function f is continuous from a until b with both of those point a being included but b not being included, than domain is ____

continuous [a,b)

60

If n is a positive interger, then limit as x approaches infinity of 1/x^n= ____ (ex. lim x approaches infinity of 1/x^2)

zero

61

A graph with lim x approaches negative infinity at -2 will have a vertical/horizontal asymptote at ___ (value) with the curve being above/below the asymptote

horizontal; -2; either

62

A graph with lim x approaches -1 from the right at infinity will have a vertical/horizontal asymptote at ___ (value) with the curve being to the right/left of the asymptote

vertical; -1; right

63

A graph with lim x approaches negative infinity of e^x is equal to ____, while a graph with lim x approaches positive infinity of e^x is equal to ____

0; infinity

64

Use the formula ______ for function of a parabla when the vertex (point touching x=0)

a(x-_)^2 +b=y, where the _ is the x coordinate at the vertex and b=0

65

Use the formula ______ for function of a parabla when the vertex (point touching x=0) is not given

a(x)^2 + bx + c =y

66

The equation x^1/3 is the same as ____

³√x (cubed root of x), just as any x^n is equilivant to the n-root of that x

67

The equation a^x is known as a _____ function, where the domain of the function is _____

exponential; all real numbers

68

One to One means that every _-value corresponds to only one _-value, i.e. passes the ____ line test

y;x;horizontal

69

If function f is one to one such that f(5)=10, than the inverse function of f such that f-1(10)= ___

5, the inverse take the solution from the original function and outputs the original f(x) value

70

The value of √27 is equal to 27^___

1/2, just as 3√27 is equal to 27^1/3, ...

71

When combining natural logarithms, give the equation ln(a) + n ln(b), you would first take _____ then _____

b to the n power; multiply the two numbers

72

When combining natural logarithms, give the equation ln(3) + 3 ln(4), you would first take _____ then _____, which equals ____

4^3; multiply 4^3 by 3; ln(192)

73

When converting radians to degrees, it is easiest to separate the standard radian (ex. pi/2, which equals ___ degrees) and multiple it by the number, so 5pi/6 = ____ degrees

90; 150, because 5(pi/6 or 30 degress)

74

When converting radians to degrees, it is easiest to separate the standard radian (ex. pi, which equals ___ degrees) and multiple it by the number, so 5pi = ____ degrees

180; 900, because 5(pi or 180 degrees)

75

When converting radians to degrees, it is easiest to separate the standard radian (ex. pi/4, which equals ___ degrees) and multiple it by the number, so 9pi/4 = ____ degrees

45; 405, because 9(pi/4 or 45 degrees)