Chapter 2 Vocab Terms Flashcards
Let n be nonnegative integer and let a(n),a(n-1),…..a(2), a(1), a(0), be real numbers with a(n) not being equal to zero. This function is given by f(x)=a(n)x(n) +a(n-1)x(n-1)=…=a(2)x(2) + a(1)x+a(0)
Polynomial Function of X of Degree of N
f(x)=a, a does not equal 0
Constant Function
f(x)=mx+b, m does not equal 0
Linear Function
Let a,b,c be real numbers with a does not equal 0. The function given by F(x)=ax^2 +bx+c
Quardratic Function
The graph of a quadratic function, u-shaped
Parabola
All parabolas are symmetric with respect to a line called the….
Axis of Symmetry
shorter name for axis of symmetry
Axis
Where axis intercepts a parabola, top or bottom of U
Vertex
Graph that has no breaks, holes, or gaps.
Continuous
Whether the graph of a polynomial function’s degree (even or odd) and by its leading coefficient, as indicated in the
Leading Coefficient Test
Relative minima or maxima
extrema
lowest (relative) point on the graph
Minima
highest (relative) point on the graph
Maxima
Point where graph intercepts the x-axis.
Zero
a factor of (x-a)^k, when k>1, yields a what kind of zero?
Repeated Zero
a factor of (x-a)^k, when k>1, x=a is related to k how? If k is odd, then the graph crosses the x-axis, If it is even the graph touches the x-axis.
Multiplicity
f(x)=(x-2) times q(x). if you know the function what do you use to find q(x)?
Long Division of Polynomials
(Dividend/Divisor)=(quotient) + (remainder?Divisor)
Division Algorithm
In F(x)/ D(x), when the degree of f(x) is greater than or equal to the degree of d(x).
Improper
In r(x)/d(x), when the degree of r(x) is less than the degree of d(x)
Proper
Short cut for using long division
Synthetic Division
The remainder obtained in the synthetic dicision process has an important interpretation as described in the….
Remainder Theorem
Theorem that states that you can test whether a polynomial has(x-k) as a factor by evaluating the polynomial at x=k, If the result is 0, then (x-k) is a factor
Factor Theorem
relates the possible rational zeros of a polynomial (having integer coefficients) to the leading coefficient and to the constant term of the polynomial
Rational Zero Test
i= the square root of -1
Imaginary Unit I
3+4i, or 2-6i, is an example of
Complex Numbers
a+bi, as opposed to bi+a
Standard form
a, in a+bi
Real Part
a+bi
Complex Number
bi, in a+bi
Imaginary Part
a number of the form bi, where b does not equal 0
Pure Imaginary Number
In the complex number system is 0, the same as the real number system. a+bi.
Additive Identity
a+bi, but we have -a-bi, it’s the what of a+bi
Addictive Inverse
a+bi , and a-bi are called what?
Complex Conjugates
If f(x) is a polynomia degree of n, where n>0, then f has at least one zero in the complex number system
Fundamental Theorem of Algebra
if f(x) is a polynomial degree of n, where n>0, then f has precisely n linear factors f(x)=a(N)(x-c(1)(x-c(2))…..(x-c(n)), where c(1) and c(2) are complex numbers
Linear Factorization Theorem
Cannot be divided by any other number besides itself and 1., has no real zeros
Prime
Prime, having no real zeros
Irreducible over the reals
can be written in the form n(x)/d(x)
Rational Function
x=a, as the function approaches infinity, or negative infinity
Vertical Asymptote
y=b,as x approaches infinity or negative infinity
Horizontal Asymptote
If the degree of the numerator is exactly on e more than the degree of the denominator, then the graph of the function has a………………
Slant of Oblique Asymptote
