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
2
Q
When slope is undefined the line is….
A
vertical
3
Q
When slope is 0 the line is….
A
horizontal
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
5
Q
an x, or vice versa that is inside the given information.
A
Linear Interpolation
6
Q
When you must predict an x value based on y or vice versa, that is not inside the data
A
Linear Extrapolation
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
8
Q
Ax+By+C=0
A
General Form
9
Q
x=a
A
vertical line
10
Q
y=b
A
horizontal line
11
Q
Two distiinct nonvertical lines when their slopes are equal, m1=m2
A
Parallel
12
Q
Two nonvertical lines thats two slopes are negative reciprocals of each other. That is, (m1)=(-1/m2)
A
Perpendicular
13
Q
two quantities that are related to each other by some rule of correspondance
A
Relation
14
Q
relation that assigns to each element x in the set A exactly one element y in the set B.
A
Function
15
Q
The set A, or set of inputs of the function f
A
Domain
16
Q
The set B, or set of outputs for the function f
A
Range
17
Q
x-value, set A,
A
input
18
Q
y-value, set B
A
output
19
Q
in y=x^2, x is the _____________ variable
A
Independent Variables
20
Q
in y+x^2, y is the___________ variable
A
Dependent Variable
21
Q
having input (x) and an output of f(x)
A
Function Notation
22
Q
set of all real numbers for which the expression is defined (found on denominator)
A
Implied Domain
23
Q
f(x+h)-f(x)/h where h does not equal zero
A
Difference Quotient
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
25
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.
Vertical line test
26
A function f is __________ on an intercal when for any x1 and x2 in the interval x1
Increasing
27
a function is ________ on an intercal when, for any x1 and x2 in the interval x1f(x2)
Decreasing
28
a function is _________ on an interval when, for any x1 and x2 in the interval f(x1)=f(x2)
Constant
29
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).
Relative Minimum
30
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)
Relative Maximum
31
greatest integer function is an example of a ________ function, whose graph resembles a set of stairsteps.
Step Function
32
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)
Even
33
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)
Odd
34
h(x)=f(x)+c
Vertical Shift Upward
35
h(x)=f(x)-c
Vertical Shift Downward
36
h(x)=f(x-c)
Horizontal Shift to the right
37
h(x)=f(x+c)
Horizontal Shift to the left
38
h(x)=-f(x)
Reflection over the x-axis
39
h(x)=f(-x)
Reflection over the y-axis
40
Horizontal Shifts, Vertical Shifts, and Reflections are called______________. Because the shape of the graph remains unchanged.
Rigid Transformations
41
cause a distortion, stretches and shrink are _________ transformations
Nonrigid Transformations
42
g(x)=cf(x), when c>1
Vertical Stretch
43
g(x)=cf(x), when 0<1
Vertical Shrink
44
h(x)=f(cx) when c>1
Horizontal Shrink
45
h(x)=f(cx) when 0<1
Horizontal Stretch
46
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)
Arithmetic Combination
47
one way to combine two functions is to form the ___________ of one with the other. f(g(x))
Composition
48
by interchanging the first and second coordinates of ordered pairs, you can form the ______________ function of f, which is denoted by f^-1
Inverse Function
49
A function f is __________ when, for a and b in its domain, f(a)=f(b) implies that a=b
One to One Function
50
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.
Horizontal Line Test
51
When y tends to increase as x increases, the graph has a __________ correlation.
Positive
52
If y tends to decrease as x increases, then the collection is said to have a ____________ correlation
Negative
53
When the points on a scatter plot do not follow any sort of pattern it is said to have....
no correlation
54
The r-value that give a measure of how well the model fits the data.
Correlation Coefficient
55
f(x)=AnX^n +A(n-1)X^(n-1) +.......A2X^2+A1X+A0
Polynomial Function of x of degreen
56
f(x)=a , a cannt equal zero.
Constant Function
57
f(x)=mx+b, m cannot equal zero
Linear Function
58
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
Quadratic Function
59
U-shaped curve that comes from graphing quadratic functions
Parabola
60
Where you can split a graph in half and it will be symmetrical on both sides
Axis of Symmetry
61
another name for Axis of Symmetry
Axis
62
The point where the axis intersects the parabola is called the _________ of the parabola
Vertex
63
Graph of polynomial has no breaks, holes, or gaps. The graph is said to be
continuous
64
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.
Leading Coefficient Test
65
Relative Maximum or Minimum
Extrema
66
Lowest relative points on a graph
Minima
67
highest relative points on a graph
Maxima
68
f(x)=d(x)q(x)+r(x)
Division Algorithm
69
f(x)/d(x) is what because f(x) is great than of equal to the degree of d(x)
Improper
70
r(x)/d(x) is what because the degree of r(x) is less than the degree of d(x)
Proper
71
shotcut for long division of polynomials
Synthetic Division
72
if f(x) is divided by (x-k) then the remainder is r = f(k)
Remiander Theorem
73
Polynomial has a factor (x-k) if and only if f(k)=0
Factor Theorem
74
relates to possible rational zeros of a polynomial = p/q, factors of constant term/ factors of leading coefficient
Rational Zero Test
75
defined as i = the square root of -1
Imiginary Unit I
76
a+bi
Complex Numbers
77
a+bi as opposed to bi+a
Standard form
78
the a, in a +bi
Real Part
79
the bi, in a +bi
Imaginary Part
80
bi
Pure Imaginary Number
81
in the complex number system is 0
Additive Identity
82
of the complex number system is a +bi
Additive Inverse
83
(a+bi) and (a-bi)
Complex Conjugates
84
Where you graph complex numbers
Complex Plane
85
(bi) y axis
Imaginary Axis
86
(a) x axis
Real Axis
87
If f(x) polynomial of degree n, where n>0, then f has at least one zero in the complex number system
Fundamental Theorem of Algebra
88
f(x)= an(x-c1)(x-c2).....(x-cn)
Linear Factorization Theorem
89
quadratic factor with no real zeros is what
Prime
90
another word for prime
Irreducible over the reals
91
f(x)= N(x)/D(x)
Rational Function
92
x=a is a __________ of the graph of f when f(x) approaches infinity, or f(x) approaches negative infinity, x=0
Vertical Asymptote
93
y=b when f(x) approaches b or as x approaches infinity or x approaches negative infinity, y=0
Horizontal Asymptote
94
If the degree of the numerator is exactly one more than the degree of the denominator, then the graph of a function has a .....
Slant of Oblique Asymptote
95
polynomial functions and rational functions
Algebraic Function
96
exponential and logarithmic functions
Transcendental Function
97
f(x)=a to the x
exponential function f with base a
98
e=2.718281828
natural base
99
f(x)=e to the x
natural Exponential Function
100
A=Pe(rt)
Continuous Compounding
101
f(x)= log a of x
Logarithmic Function with base a
102
base 10, f(x)=log 10 of x
Common Logarithmic Function
103
f(x)=lnx
natural Logarithmic Function
104
log a of x can be converted to evaluate logarithms of other bases
Change of Base Formula
105
y=ae to the bx when b>0
Exponential Growht Model
106
y=ae to the -bx when b>0
Exponential Decay Model
107
y=ae -(x-b)^2/c
Guassian Model
108
y=a/1+be^-rx
Logistic Growth Model
109
y= a+b lnx, or y=a +b log10 of x
Logarithmic Model
110
term used to describe Guassian models
normally distributed
111
curve that gaussian models have.
Bell-shaped curve
112
curve of logistic function
Logistic Curve
113
another name for logistic curve
Sigmoidal Curve
