1st Semester Review Vocab Terms Flashcards
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
Slope
When slope is undefined the line is….
vertical
When slope is 0 the line is….
horizontal
y-y1=m(x-x1), equation of line that passes through point (x,y) and has a slope of m.
Point Slope Form
an x, or vice versa that is inside the given information.
Linear Interpolation
When you must predict an x value based on y or vice versa, that is not inside the data
Linear Extrapolation
graph of the equation y=mx+b, is a line whose slope is m and whose y intercept is (o,b)
Slope-Intercept Form
Ax+By+C=0
General Form
x=a
vertical line
y=b
horizontal line
Two distiinct nonvertical lines when their slopes are equal, m1=m2
Parallel
Two nonvertical lines thats two slopes are negative reciprocals of each other. That is, (m1)=(-1/m2)
Perpendicular
two quantities that are related to each other by some rule of correspondance
Relation
relation that assigns to each element x in the set A exactly one element y in the set B.
Function
The set A, or set of inputs of the function f
Domain
The set B, or set of outputs for the function f
Range
x-value, set A,
input
y-value, set B
output
in y=x^2, x is the _____________ variable
Independent Variables
in y+x^2, y is the___________ variable
Dependent Variable
having input (x) and an output of f(x)
Function Notation
set of all real numbers for which the expression is defined (found on denominator)
Implied Domain
f(x+h)-f(x)/h where h does not equal zero
Difference Quotient
is the collection of ordered pairs (x,f(x)), such that x is in the domain of f. (visual)
Graph of a Function
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
A function f is __________ on an intercal when for any x1 and x2 in the interval x1<f(x2)
Increasing
a function is ________ on an intercal when, for any x1 and x2 in the interval x1f(x2)
Decreasing
a function is _________ on an interval when, for any x1 and x2 in the interval f(x1)=f(x2)
Constant
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
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
greatest integer function is an example of a ________ function, whose graph resembles a set of stairsteps.
Step Function
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
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
h(x)=f(x)+c
Vertical Shift Upward
h(x)=f(x)-c
Vertical Shift Downward
h(x)=f(x-c)
Horizontal Shift to the right
h(x)=f(x+c)
Horizontal Shift to the left
h(x)=-f(x)
Reflection over the x-axis
h(x)=f(-x)
Reflection over the y-axis
Horizontal Shifts, Vertical Shifts, and Reflections are called______________. Because the shape of the graph remains unchanged.
Rigid Transformations
cause a distortion, stretches and shrink are _________ transformations
Nonrigid Transformations
g(x)=cf(x), when c>1
Vertical Stretch
g(x)=cf(x), when 0<1
Vertical Shrink
h(x)=f(cx) when c>1
Horizontal Shrink
h(x)=f(cx) when 0<1
Horizontal Stretch
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
one way to combine two functions is to form the ___________ of one with the other. f(g(x))
Composition
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
A function f is __________ when, for a and b in its domain, f(a)=f(b) implies that a=b
One to One Function
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
When y tends to increase as x increases, the graph has a __________ correlation.
Positive
If y tends to decrease as x increases, then the collection is said to have a ____________ correlation
Negative
When the points on a scatter plot do not follow any sort of pattern it is said to have….
no correlation
The r-value that give a measure of how well the model fits the data.
Correlation Coefficient
f(x)=AnX^n +A(n-1)X^(n-1) +…….A2X^2+A1X+A0
Polynomial Function of x of degreen
f(x)=a , a cannt equal zero.
Constant Function
f(x)=mx+b, m cannot equal zero
Linear Function
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
U-shaped curve that comes from graphing quadratic functions
Parabola
Where you can split a graph in half and it will be symmetrical on both sides
Axis of Symmetry
another name for Axis of Symmetry
Axis
The point where the axis intersects the parabola is called the _________ of the parabola
Vertex
Graph of polynomial has no breaks, holes, or gaps. The graph is said to be
continuous
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
Relative Maximum or Minimum
Extrema
Lowest relative points on a graph
Minima
highest relative points on a graph
Maxima
f(x)=d(x)q(x)+r(x)
Division Algorithm
f(x)/d(x) is what because f(x) is great than of equal to the degree of d(x)
Improper
r(x)/d(x) is what because the degree of r(x) is less than the degree of d(x)
Proper
shotcut for long division of polynomials
Synthetic Division
if f(x) is divided by (x-k) then the remainder is r = f(k)
Remiander Theorem
Polynomial has a factor (x-k) if and only if f(k)=0
Factor Theorem
relates to possible rational zeros of a polynomial = p/q, factors of constant term/ factors of leading coefficient
Rational Zero Test
defined as i = the square root of -1
Imiginary Unit I
a+bi
Complex Numbers
a+bi as opposed to bi+a
Standard form
the a, in a +bi
Real Part
the bi, in a +bi
Imaginary Part
bi
Pure Imaginary Number
in the complex number system is 0
Additive Identity
of the complex number system is a +bi
Additive Inverse
(a+bi) and (a-bi)
Complex Conjugates
Where you graph complex numbers
Complex Plane
(bi) y axis
Imaginary Axis
(a) x axis
Real Axis
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
f(x)= an(x-c1)(x-c2)…..(x-cn)
Linear Factorization Theorem
quadratic factor with no real zeros is what
Prime
another word for prime
Irreducible over the reals
f(x)= N(x)/D(x)
Rational Function
x=a is a __________ of the graph of f when f(x) approaches infinity, or f(x) approaches negative infinity, x=0
Vertical Asymptote
y=b when f(x) approaches b or as x approaches infinity or x approaches negative infinity, y=0
Horizontal Asymptote
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
polynomial functions and rational functions
Algebraic Function
exponential and logarithmic functions
Transcendental Function
f(x)=a to the x
exponential function f with base a
e=2.718281828
natural base
f(x)=e to the x
natural Exponential Function
A=Pe(rt)
Continuous Compounding
f(x)= log a of x
Logarithmic Function with base a
base 10, f(x)=log 10 of x
Common Logarithmic Function
f(x)=lnx
natural Logarithmic Function
log a of x can be converted to evaluate logarithms of other bases
Change of Base Formula
y=ae to the bx when b>0
Exponential Growht Model
y=ae to the -bx when b>0
Exponential Decay Model
y=ae -(x-b)^2/c
Guassian Model
y=a/1+be^-rx
Logistic Growth Model
y= a+b lnx, or y=a +b log10 of x
Logarithmic Model
term used to describe Guassian models
normally distributed
curve that gaussian models have.
Bell-shaped curve
curve of logistic function
Logistic Curve
another name for logistic curve
Sigmoidal Curve
