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Precalc Final > Study > Flashcards

Study Flashcards

1
Q

What does a^-n also equal?

A

1/a^n

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2
Q

Also equals 1/a^2

A

a^-n

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3
Q

(a • b)^2 equals

A

a^n • b^n

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4
Q

(a/b)^n equals

A

a^n/b^n

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5
Q

(a/b)^-n equals

A

(b/a)^n

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6
Q

A^3-B^3 =

A

(A-B)(A^2+AB+B^2)

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7
Q

(A-B)(A^2+AB+B^2) =

A

A^3-B^3

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8
Q

A^3+B^3 =

A

(A+B)(A^2-AB+B^2)

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9
Q

(A+B)(A^2-AB+B^2)

A

A^3+B^3

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10
Q

7 √20 =

A

7 √4•5 = 14 √5

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11
Q

Zero product property

A

If A and B are two expressions, AB=0 iff A=0 or B=0

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12
Q

If A and B are two expressions, AB=0 iff A=0 or B=0

A

Zero product property

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13
Q

How do you complete the square?

A

Take b/2 and square it. Then add that to the equation and keep any extra constants on right side

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14
Q

Take b/2 and square it. Then add that to the equation and keep any extra constants on right si

A

Completing the square

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15
Q

When do you check if a problem has no solutions with a value of x?

A

When the problem is a rational expression (denominators) or you squared both sides

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16
Q

When a problem has rational expressions (denominators) or you square both sides you

A

Check the values of x to make sure they don’t have no solution

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17
Q

Domain of inequality

A

Set of real numbers at which it can be evaluated

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18
Q

Set of real numbers at which an inequality can be evaluated

A

Domain

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19
Q

Solution set of an inequality

A

Set of real numbers that make it true

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20
Q

Set of real numbers that make an inequality true

A

Solution set

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21
Q

A combination of one or more inequalities

A

Compound inequality

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22
Q

Compound inequality

A

A combination of one or more inequalities

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23
Q

Distance between two points formula

A

√(x1-x2)^2 + (y1-y2)^2

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24
Q

Midpoint between two points formula

A

(x1+x2/2 , y1+y2/2)

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25
Q

√(x1-x2)^2 + (y1-y2)^2

A

Distance formula between two points

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26
Q

(x1+x2/2 , y1+y2/2)

A

Midpoint between two points formula

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27
Q

How can you tell if a linear equation is symmetric over the y-axis?

A

Replace x with -x

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28
Q

Replace x with -x

A

To tell if a linear equation is symmetric over y-axis

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29
Q

Circle standard equation

A

(X-h)^2 + (y-k)^2 = r^2

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30
Q

Point slope formula

A

y-y1 = m(x-x1)

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31
Q

y-y1 = m(x-x1)

A

Point slope formula

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32
Q

Negative reciprocal slope formula

A

m1 • m2 = -1

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33
Q

m1 • m2 = -1

A

Negative reciprocal slope formula

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34
Q

How to tell if a function is even?

A

Place -x in for x and see if it is the same function

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35
Q

Place -x in for x and see if it is the same function

A

To tell if a function is even

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36
Q

When is the graph of a function even?

A

Symmetric over y-axis

37
Q

If the graph of a function is symmetric over y-axis

A

Even function

38
Q

Polynomial with all degrees even

A

Even function

39
Q

Polynomial with all odd degrees

A

Odd function

40
Q

Polynomial with neither all even nor all odd degrees

A

Neither even or odd function

41
Q

Neither even or odd function

A

Polynomial with neither all even nor all odd degrees

42
Q

Average rate of change formula

A

Same as slope formula

43
Q

Same as slope formula

A

Average rate of change formula

44
Q

The graph of a function is neither even nor odd if

A

Symmetric across x-axis

45
Q

If a function is symmetric across x-axis

A

Neither even nor odd function

46
Q

A function is one to one iff

A

x=f^-1(y) iff y=f(x)

47
Q

f^-1(f(x)) =

A

x

48
Q

f(f^-1(x)) =

A

x

49
Q

Vertex form

A

f(x)=a(x-h)^2 + k where (h,k) is the vertex

50
Q

f(x)=a(x-h)^2 + k where (h,k) is the vertex

A

Vertex form

51
Q

Properties of a polynomial

A

Nonnegative exponents and defined on all reals (-∞, ∞)

52
Q

Nonnegative exponents and defined on all reals (-∞, ∞)

A

Properties of polynomials

53
Q

How to find the vertex of a quadratic

A

(-b/2a, f(-b/2a))

54
Q

(-b/2a, f(-b/2a))

A

How to find the vertex of a quadratic

55
Q

What horizontal asymptote does this have?

f(x) = 5x+2/1-3x

A

y=-5/3 because equal degrees so determined by leading coefficients

56
Q

What horizontal asymptote does this have?

2x/x^2 +1

A

y=0 because bottom is bigger degree

57
Q

What horizontal asymptote does this have?

3x^2 -1/x+2

A

None because top degree is bigger

58
Q

When does a function touch x-axis?

A

Even multiplicity

59
Q

When does a function cross the x-axis?

A

Odd multiplicity

60
Q

Compound interest formula

A

A=P(1+r/n)^nt where a is amount, P is principal, r is # of compounds per year, t is time

61
Q

A=P(1+r/n)^nt

A

Compound interest formula

62
Q

Continuously compounded interest formula

A

A=Pe^rt

63
Q

A=Pe^rt

A

Continuously compounded interest formula

64
Q

Exponential growth and decay formula

A

A(t)=A(o)e^kt where A(t) is amount after time (t), A(o) is initial amount, k is relative rate of growth, t is time

65
Q

A(t)=A(o)e^kt

A

Exponential growth and decay formula

66
Q

what does the graph of log(a)x where a is any integer look like?

A

Point at (1,0) and (a,1)

67
Q

How is 4^3=64 solved?

A

3=log(4)64

68
Q

Evaluate log(5)25

A

log(5)(5^2) = 2

69
Q

Evaluate log(1/3)9

A

log(1/3)(3^2) =

log(1/3)((1/3)^-1)^2 = -2

70
Q

Evaluate log(4)1/2

A

log(4)(4^-1/2) = -1/2

71
Q

What does h equal in the half life formula?

A

h=-ln2/k

72
Q

h=-ln2/k

A

H in half life formula

73
Q

What is always true about the value of k in a half life formula?

A

It is negative

74
Q

Always negative in half life formula

A

k

75
Q

What is done first here?

3^x - 8 • 3^-x = 2

A

Multiply both sides by 3^x to get rid of negative exponent

76
Q

For .7^x<3, what’s the difference between taking the log(.7) of both sides and taking the ln of both sides?

A

Ln stays on left side and is divided in the end while log operated on only right side

77
Q

When is an angle in standard position?

A

When its vertex is at the origin and it’s initial side lies along the positive x-axis

78
Q

When its vertex is at the origin and it’s initial side lies along the positive x-axis

A

When an angle is in standard position

79
Q

The radian measure of an angle θ is

A

The length of the arc it subtends in the unit circle

80
Q

Arc length formula

A

S=rθ where S is arc length and r is radius

81
Q

S=rθ

A

Arc length formula

82
Q

Linear velocity arc length

A

v=S/t

83
Q

v=S/t

A

Linear velocity arc length

84
Q

Angular velocity arc length

A

w= θ/t

85
Q

w= θ/t

A

Angular velocity arc length

86
Q

Rotations per minute is handled how?

A

Multiplied by 2π

87
Q

Linear and angular speed formula

A

v=rw

88
Q

v=rw

A

Linear and angular speed formula

Precalc Final (1 decks)

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