Exam 1 Flashcards

1
Q

define relation

A

set of ordered pairs

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2
Q

define domain

A

set of the first components of the ordered pairs

x

input

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3
Q

define range

A

set of the second components of ordered pairs

y

output

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4
Q

define range

A

set of the second components of ordered pairs

y

output

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5
Q

2 ways to express relations

A

equations

graphs

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6
Q

define function

A

a relation where each domain value (x) is paired with only one range value (y)

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7
Q

in function equations, the y value must be able to be…

A

isolated on one side

raised to the first power only

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8
Q

on graphs, a function must pass the ….

A

vertical line test

any vertical line you could possibly draw on the plane must only intersect the graph one time

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9
Q

non-example of a function

A

circle

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10
Q

function notation

A

f(x) = y

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11
Q

set notation for “y is greater than or equal to 0”

A

{y|y ≥ 0}

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12
Q

“ | ” means…

A

“such that”

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13
Q

define interval

A

single unbroken set of numbers in a line

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14
Q

steps of using interval notation

A

list leftmost & rightmost boundaries w/ comma between

check if boundaries are part of interval & use ( ) or []

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15
Q

in interval notation, “( )” means…

A

that boundary is not included

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16
Q

in interval notation, “[]” means…

A

that boundary is included

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17
Q

if there is no upper or lower boundary, use…

A

(+/- oo)

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18
Q

if you consider 2 intervals as part of the same set…

A

use a union

U

ex. (4, oo) U [0, 3)

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19
Q

define natural numbers

A

1, 2, 3, 4, 5, 6….

no zero

no negatives

no fractions

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20
Q

define whole numbers

A

naturals + zero

no negatives

no fractions

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21
Q

define integers

A

whole numbers + negatives

no fractions

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22
Q

define rational numbers

A

integers and fractions involving integers

includes terminating & repeating decimals

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23
Q

define irrational numbers

A

cannot be written as a fraction of integers

includes non-repeating, non-terminating decimals

ex. pi, square root of 2, etc

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24
Q

define real numbers

A

union of rational & irrational numbers

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25
Q

(A + B) + C = A + (B + C)

A(BC) = AB(C)

A

associativity

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26
Q

A + B = B + A

AB = BA

A

commutativity

27
Q

A(B + C) = AB + AC

A

distribution

28
Q

A + 0 = A

1A = A

A

identity

29
Q

define coefficient

A

* variable

30
Q

define expression

A

terms added & subtracted together

31
Q

define term

A

collection of variables & numbers multiplied & divided together

32
Q

define equation

A

2 expressions w/ an equal sign between

33
Q

define linear

A

describes a term, expression, or equation where…

  • each term has one variable or less
  • variables are raised only to the first power
34
Q

define compound inequality

A

combination of 2 inequality statements

35
Q

2 types of compound inequalities

A

intersection

union

36
Q

define intersection

A

a set of values present in one set AND the other

37
Q

define union

A

set with values present in one set OR the other

38
Q

which compound inequality has overlap?

which has a gap?

A

overlap - intersection

gap - union

39
Q

x = all real numbers in interval notation

A

(-oo, oo)

40
Q

what makes linear functions unique?

A

they have a constant rate of change between inputs & outputs

41
Q

every linear function has…

A

a slope

42
Q

m =

A

slope

43
Q

SLOPE EQUATION

A
44
Q

what is necessary to calculate slope?

A

2 ordered pairs

45
Q

a slope of - ⅔ indicates that…

A
  • the line runs downward (-)
  • it takes 2 units in x to move down 3 units in y
46
Q

to uniquely determine a linear function, we need…

A

slope

an ordered pair for the function

47
Q

b =

A

the initial value of f(x)

f(o)

the y-intercept

48
Q

LINEAR FUNCTION EQUATION

A
49
Q

to find x intercept…

A

place 0 in for y

50
Q

to find y intercept…

A

place 0 in for x

51
Q

how to generate an ordered pair using slope

A

rise + a y-value and run + an x-value = an ordered pair

52
Q

slopes of perpendicular lines

A

negative reciprocal

53
Q

formula for vertical lines

A

x = z

54
Q

formula for horizontal lines

A

y = b

55
Q

product rule

A

am * an = am+n

56
Q

zero rule

A

a0 = 1

57
Q

quotient rule

A

am/an = am-n

58
Q

negative rule (2)

A

a-n = 1/an

1/a-n = an

59
Q

power rule (3)

A
  • (am)n = amn
  • (ab)n = anbn
  • (a/b)n = an/bn
60
Q

define polynomial

A

expression made of terms whose variables are raised to natural powers

61
Q

degree of a polynomial

A

greatest exponent

62
Q

leading term

A

term with the greatest variable

63
Q

leading coefficient

A

coefficient of the leading term

64
Q

shortcuts for full polynomial multiplication

A

FOIL

each term * each term