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