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Pre Calc > 1st Semester Review Vocab Terms > Flashcards

1st Semester Review Vocab Terms Flashcards

1
Q

M of the nonvertical line through (x1,y1) and (x2, y2) is m=y2-y1/x2-x1=change in y/ change in x, where x’s do NOT equal each other

A

Slope

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2
Q

When slope is undefined the line is….

A

vertical

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3
Q

When slope is 0 the line is….

A

horizontal

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4
Q

y-y1=m(x-x1), equation of line that passes through point (x,y) and has a slope of m.

A

Point Slope Form

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5
Q

an x, or vice versa that is inside the given information.

A

Linear Interpolation

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6
Q

When you must predict an x value based on y or vice versa, that is not inside the data

A

Linear Extrapolation

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7
Q

graph of the equation y=mx+b, is a line whose slope is m and whose y intercept is (o,b)

A

Slope-Intercept Form

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8
Q

Ax+By+C=0

A

General Form

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9
Q

x=a

A

vertical line

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10
Q

y=b

A

horizontal line

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11
Q

Two distiinct nonvertical lines when their slopes are equal, m1=m2

A

Parallel

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12
Q

Two nonvertical lines thats two slopes are negative reciprocals of each other. That is, (m1)=(-1/m2)

A

Perpendicular

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13
Q

two quantities that are related to each other by some rule of correspondance

A

Relation

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14
Q

relation that assigns to each element x in the set A exactly one element y in the set B.

A

Function

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15
Q

The set A, or set of inputs of the function f

A

Domain

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16
Q

The set B, or set of outputs for the function f

A

Range

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17
Q

x-value, set A,

A

input

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18
Q

y-value, set B

A

output

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19
Q

in y=x^2, x is the _____________ variable

A

Independent Variables

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20
Q

in y+x^2, y is the___________ variable

A

Dependent Variable

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21
Q

having input (x) and an output of f(x)

A

Function Notation

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22
Q

set of all real numbers for which the expression is defined (found on denominator)

A

Implied Domain

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23
Q

f(x+h)-f(x)/h where h does not equal zero

A

Difference Quotient

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24
Q

is the collection of ordered pairs (x,f(x)), such that x is in the domain of f. (visual)

A

Graph of a Function

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25
Q

at most one y-value corresponds to a given x-value. It then follows the vertical line can intersect the graph of a function at most once. Set of points of coordinates plane is the graph of y as a function of x if and only if no vertical line intersects the graph at mroe than one point.

A

Vertical line test

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26
Q

A function f is __________ on an intercal when for any x1 and x2 in the interval x1<f(x2)

A

Increasing

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27
Q

a function is ________ on an intercal when, for any x1 and x2 in the interval x1f(x2)

A

Decreasing

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28
Q

a function is _________ on an interval when, for any x1 and x2 in the interval f(x1)=f(x2)

A

Constant

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29
Q

function value f is called _______ of f when there exists an intercal (x1,x2) that contains a such that x1< or equal to f(x).

A

Relative Minimum

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30
Q

function value f is called the __________ of f when there exists an interval (x1,x2) that contains a such that x1 or equal to f(x)

A

Relative Maximum

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31
Q

greatest integer function is an example of a ________ function, whose graph resembles a set of stairsteps.

A

Step Function

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32
Q

a function whose graph is symmetric with resepect to the y-axis is a _______ function. for each x in the domain of f, f(-x)=f(x)

A

Even

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33
Q

a function whose graph is symmetric with respect to the origin is an ________ function. for each x in the domain of f,f(-x)= -f(x)

A

Odd

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34
Q

h(x)=f(x)+c

A

Vertical Shift Upward

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35
Q

h(x)=f(x)-c

A

Vertical Shift Downward

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36
Q

h(x)=f(x-c)

A

Horizontal Shift to the right

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37
Q

h(x)=f(x+c)

A

Horizontal Shift to the left

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38
Q

h(x)=-f(x)

A

Reflection over the x-axis

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39
Q

h(x)=f(-x)

A

Reflection over the y-axis

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40
Q

Horizontal Shifts, Vertical Shifts, and Reflections are called______________. Because the shape of the graph remains unchanged.

A

Rigid Transformations

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41
Q

cause a distortion, stretches and shrink are _________ transformations

A

Nonrigid Transformations

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42
Q

g(x)=cf(x), when c>1

A

Vertical Stretch

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43
Q

g(x)=cf(x), when 0<1

A

Vertical Shrink

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44
Q

h(x)=f(cx) when c>1

A

Horizontal Shrink

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45
Q

h(x)=f(cx) when 0<1

A

Horizontal Stretch

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46
Q

domain of these, of function f and g consist of all real numbers that are common to the domains of f and g. such as f(x)/g(x)

A

Arithmetic Combination

47
Q

one way to combine two functions is to form the ___________ of one with the other. f(g(x))

A

Composition

48
Q

by interchanging the first and second coordinates of ordered pairs, you can form the ______________ function of f, which is denoted by f^-1

A

Inverse Function

49
Q

A function f is __________ when, for a and b in its domain, f(a)=f(b) implies that a=b

A

One to One Function

50
Q

To find out if a graph is one to one, you use this test. Check to see that every horizontal line intersects the graph of the function at most once.

A

Horizontal Line Test

51
Q

When y tends to increase as x increases, the graph has a __________ correlation.

A

Positive

52
Q

If y tends to decrease as x increases, then the collection is said to have a ____________ correlation

A

Negative

53
Q

When the points on a scatter plot do not follow any sort of pattern it is said to have….

A

no correlation

54
Q

The r-value that give a measure of how well the model fits the data.

A

Correlation Coefficient

55
Q

f(x)=AnX^n +A(n-1)X^(n-1) +…….A2X^2+A1X+A0

A

Polynomial Function of x of degreen

56
Q

f(x)=a , a cannt equal zero.

A

Constant Function

57
Q

f(x)=mx+b, m cannot equal zero

A

Linear Function

58
Q

Let a,b, and c be real numbers with a not equalling zero. The function is given by f(x)=a(x)^2+b(x)+c

A

Quadratic Function

59
Q

U-shaped curve that comes from graphing quadratic functions

A

Parabola

60
Q

Where you can split a graph in half and it will be symmetrical on both sides

A

Axis of Symmetry

61
Q

another name for Axis of Symmetry

A

Axis

62
Q

The point where the axis intersects the parabola is called the _________ of the parabola

A

Vertex

63
Q

Graph of polynomial has no breaks, holes, or gaps. The graph is said to be

A

continuous

64
Q

Whether the graph of a polynomial eventually rises or falls can be determined by the polynomial function’s degree (even or odd) and by its leading coefficient, as indicated in the Leading Coefficient Test.

A

Leading Coefficient Test

65
Q

Relative Maximum or Minimum

A

Extrema

66
Q

Lowest relative points on a graph

A

Minima

67
Q

highest relative points on a graph

A

Maxima

68
Q

f(x)=d(x)q(x)+r(x)

A

Division Algorithm

69
Q

f(x)/d(x) is what because f(x) is great than of equal to the degree of d(x)

A

Improper

70
Q

r(x)/d(x) is what because the degree of r(x) is less than the degree of d(x)

A

Proper

71
Q

shotcut for long division of polynomials

A

Synthetic Division

72
Q

if f(x) is divided by (x-k) then the remainder is r = f(k)

A

Remiander Theorem

73
Q

Polynomial has a factor (x-k) if and only if f(k)=0

A

Factor Theorem

74
Q

relates to possible rational zeros of a polynomial = p/q, factors of constant term/ factors of leading coefficient

A

Rational Zero Test

75
Q

defined as i = the square root of -1

A

Imiginary Unit I

76
Q

a+bi

A

Complex Numbers

77
Q

a+bi as opposed to bi+a

A

Standard form

78
Q

the a, in a +bi

A

Real Part

79
Q

the bi, in a +bi

A

Imaginary Part

80
Q

bi

A

Pure Imaginary Number

81
Q

in the complex number system is 0

A

Additive Identity

82
Q

of the complex number system is a +bi

A

Additive Inverse

83
Q

(a+bi) and (a-bi)

A

Complex Conjugates

84
Q

Where you graph complex numbers

A

Complex Plane

85
Q

(bi) y axis

A

Imaginary Axis

86
Q

(a) x axis

A

Real Axis

87
Q

If f(x) polynomial of degree n, where n>0, then f has at least one zero in the complex number system

A

Fundamental Theorem of Algebra

88
Q

f(x)= an(x-c1)(x-c2)…..(x-cn)

A

Linear Factorization Theorem

89
Q

quadratic factor with no real zeros is what

A

Prime

90
Q

another word for prime

A

Irreducible over the reals

91
Q

f(x)= N(x)/D(x)

A

Rational Function

92
Q

x=a is a __________ of the graph of f when f(x) approaches infinity, or f(x) approaches negative infinity, x=0

A

Vertical Asymptote

93
Q

y=b when f(x) approaches b or as x approaches infinity or x approaches negative infinity, y=0

A

Horizontal Asymptote

94
Q

If the degree of the numerator is exactly one more than the degree of the denominator, then the graph of a function has a …..

A

Slant of Oblique Asymptote

95
Q

polynomial functions and rational functions

A

Algebraic Function

96
Q

exponential and logarithmic functions

A

Transcendental Function

97
Q

f(x)=a to the x

A

exponential function f with base a

98
Q

e=2.718281828

A

natural base

99
Q

f(x)=e to the x

A

natural Exponential Function

100
Q

A=Pe(rt)

A

Continuous Compounding

101
Q

f(x)= log a of x

A

Logarithmic Function with base a

102
Q

base 10, f(x)=log 10 of x

A

Common Logarithmic Function

103
Q

f(x)=lnx

A

natural Logarithmic Function

104
Q

log a of x can be converted to evaluate logarithms of other bases

A

Change of Base Formula

105
Q

y=ae to the bx when b>0

A

Exponential Growht Model

106
Q

y=ae to the -bx when b>0

A

Exponential Decay Model

107
Q

y=ae -(x-b)^2/c

A

Guassian Model

108
Q

y=a/1+be^-rx

A

Logistic Growth Model

109
Q

y= a+b lnx, or y=a +b log10 of x

A

Logarithmic Model

110
Q

term used to describe Guassian models

A

normally distributed

111
Q

curve that gaussian models have.

A

Bell-shaped curve

112
Q

curve of logistic function

A

Logistic Curve

113
Q

another name for logistic curve

A

Sigmoidal Curve

Pre Calc (4 decks)

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