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Trig > Mid Term > Flashcards

Mid Term Flashcards

1
Q

When is a system consistent?

A

If it has at least one solution

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2
Q

When is a system independent?

A

When it has exactly one solution

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3
Q

When is a system dependent?

A

When it has infinitely many solutions

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4
Q

When is a system inconsistent?

A

When it has no solutions (no point of intersection)

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5
Q

What does it mean when the symmetry is odd?

A

It has origin symmetry

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6
Q

What does it mean when the symmetry is even?

A

It has y-axis symmetry

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7
Q

How do you find the VA?

A

Set the denom. Equal to 0

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8
Q

How do you find HA?

A

Look at the powers

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9
Q

What is the HA when the higher power is on the denom.

A

It equals 0

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10
Q

What happens when the higher power is in the numerator?

A

There is no HA

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11
Q

How do you find the OA?

A

Long division

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12
Q

How do you find the x-axis?

A

Set the top equal to zero

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13
Q

How do you find the y-axis?

A

set all the x’s equal to zero

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14
Q

What is a relation?

A

Any pairing between two sets

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15
Q

What is a function?

A

A relation where every x is paired with one y

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16
Q

What is a radicand?

A

Things inside the parenthesis

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17
Q

What is composition?

A

Putting functions together

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18
Q

When you have f(g(x)) which do you put in which?

A

G goes into f

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19
Q

What is the zero if a function?

A

X-int

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20
Q

What is a reciprocal?

A

2 numbers that multiply to equal 1

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21
Q

What is point slope equation?

A

y-y1=m(x-x1)

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22
Q

What are parallel lines?

A

The same slope but different y-int

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23
Q

What are coinciding lines?

A

Infinitely many points in common, same slope same y-int

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24
Q

What are perpendicular lines?

A

Opposite reciprocal slope different y-int

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25
Q

What are the two variations of the answer to systems of equations?

A

Ordered pair and common solution to both equations

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26
Q

Which way do you shade when >?

A

Above or to the right

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27
Q

What is linear combination

A

Systems of equations, addition or elimination

28
Q

How do you solve three variable eqn.?

A

Eliminate from two of them

Eliminate the same variable from two others

Use the solution eqn. And eliminate from those

Plug answer into one of the most recent eqn.

Plug both answers into one of the beginning eqn.

29
Q

What is origin symmetry?

A

(x,y)=(-x,-y)

30
Q

What is y-axis symmetry?

A

(x,y)=(-x,y)

31
Q

What is x-axis symmetry?

A

(x,y)=(x,-y)

32
Q

What is y=x symmetry?

A

(x,y)=(y,x)

33
Q

What is y=-x symmetry?

A

(x,y)=(-y,-x)

34
Q

Why is there no name for a function with x-axis symmetry?

A

Because if it has x-axis symmetry then it isn’t a function

35
Q

Reflections

A

Flips

36
Q

Transformations

A

Shifts

37
Q

Dilations

A

Steepness

38
Q

What kind of symmetry do inverses have?

A

y=x

39
Q

When will the inverse of f(x) be a function?

A

Only if f(x) passes the horizontal line test

40
Q

How do you write an inverse of a function?

A
  1. ) write the original as “y=….”
  2. ) switch x and y
  3. ) solve for y
  4. ) rename as f-1(x)
41
Q

True or false: you can add square roots and get the correct answer

A

False

42
Q

True or false: you can multiply square roots and get the right answer

A

True

43
Q

What are the powers of i?

A

i = the square root of -1
i squared = -1
i cubed = -i
i to the fourth = 1

44
Q

True or false: polynomial functions have positive integer exponents on the variables

A

True

45
Q

True or false: polynomial functions have exponents on variables

A

False

46
Q

True or false: polynomial functions have no variables in the denom.

A

True

47
Q

True or false: polynomial functions have no rational exponents

A

True

48
Q

True or false: polynomial functions have variables under roots

A

False

49
Q

True or false: polynomial functions have any things as coefficients

A

True

50
Q

What is the degree of a polynomial?

A

Highest exponent of any individual variable term

51
Q

What is the lead coefficient of a polynomial?

A

Coefficient of the highest power term

52
Q

What four things mean the same thing?

A

Roots
Zeros
x-int
Solutions

53
Q

How many roots do 1st degree roots have?

A

1 real

54
Q

How many roots do 2nd degree roots have?

A

2 real or 2 imag. Or 1 double root

55
Q

How many roots do 3rd degree roots have?

A

3 reals or 1 single 1 double or 1 real 2 imag. Or 1 triple

56
Q

ax squared is what?

A

The quadratic term

57
Q

bx is what?

A

The linear term

58
Q

c is what?

A

The constant

59
Q

What are the five ways to solve a quadratic eqn.?

A
  1. ) Factoring (only works on some)
  2. ) quadratic formula (works on all)
  3. ) completing the square (works on all but can get messy)
  4. ) GCF (only if constant term is missing)
  5. ) direct attack (if linear term is missing)
60
Q

Steps to complete the square

A
  1. ) move constant to the other side
  2. ) quadratic coefficient must be 1
  3. ) half the linear coefficient square it add it to both sides
  4. ) factor into a binomial (should work perfectly)
  5. ) Solve for x
61
Q

What does the discriminant determine?

A

How many and what kind of roots a quad. Eqn. Has

62
Q

If D>0

A

2 real roots

63
Q

If D=0

A

1 real double root

64
Q

What is the conjugate root theorem?

A

If a+bi is a root of an eqn. Then a-bi must also be a root of the eqn.

65
Q

If 5+3i/7 is a root of an eqn. What must be another root?

A

5-3i/7

Trig (2 decks)

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