Chapter 2 Vocab Terms

Question 1

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)

Answer 1

Polynomial Function of X of Degree of N

Question 2

f(x)=a, a does not equal 0

Answer 2

Constant Function

Question 3

f(x)=mx+b, m does not equal 0

Answer 3

Linear Function

Question 4

Let a,b,c be real numbers with a does not equal 0. The function given by F(x)=ax^2 +bx+c

Answer 4

Quardratic Function

Question 5

The graph of a quadratic function, u-shaped

Answer 5

Parabola

Question 6

All parabolas are symmetric with respect to a line called the….

Answer 6

Axis of Symmetry

Question 7

shorter name for axis of symmetry

Answer 7

Axis

Question 8

Where axis intercepts a parabola, top or bottom of U

Answer 8

Vertex

Question 9

Graph that has no breaks, holes, or gaps.

Answer 9

Continuous

Question 10

Whether the graph of a polynomial function’s degree (even or odd) and by its leading coefficient, as indicated in the

Answer 10

Leading Coefficient Test

Question 11

Relative minima or maxima

Answer 11

extrema

Question 12

lowest (relative) point on the graph

Answer 12

Minima

Question 13

highest (relative) point on the graph

Answer 13

Maxima

Question 14

Point where graph intercepts the x-axis.

Answer 14

Zero

Question 15

a factor of (x-a)^k, when k>1, yields a what kind of zero?

Answer 15

Repeated Zero

Question 16

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.

Answer 16

Multiplicity

Question 17

f(x)=(x-2) times q(x). if you know the function what do you use to find q(x)?

Answer 17

Long Division of Polynomials

Question 18

(Dividend/Divisor)=(quotient) + (remainder?Divisor)

Answer 18

Division Algorithm

Question 19

In F(x)/ D(x), when the degree of f(x) is greater than or equal to the degree of d(x).

Answer 19

Improper

Question 20

In r(x)/d(x), when the degree of r(x) is less than the degree of d(x)

Answer 20

Proper

Question 21

Short cut for using long division

Answer 21

Synthetic Division

Question 22

The remainder obtained in the synthetic dicision process has an important interpretation as described in the….

Answer 22

Remainder Theorem

Question 23

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

Answer 23

Factor Theorem

Question 24

relates the possible rational zeros of a polynomial (having integer coefficients) to the leading coefficient and to the constant term of the polynomial

Answer 24

Rational Zero Test

Question 25

i= the square root of -1

Answer 25

Imaginary Unit I

Question 26

3+4i, or 2-6i, is an example of

Answer 26

Complex Numbers

Question 27

a+bi, as opposed to bi+a

Answer 27

Standard form

Question 28

a, in a+bi

Answer 28

Real Part

Question 29

a+bi

Answer 29

Complex Number

Question 30

bi, in a+bi

Answer 30

Imaginary Part

Question 31

a number of the form bi, where b does not equal 0

Answer 31

Pure Imaginary Number

Question 32

In the complex number system is 0, the same as the real number system. a+bi.

Answer 32

Additive Identity

Question 33

a+bi, but we have -a-bi, it's the what of a+bi

Answer 33

Addictive Inverse

Question 34

a+bi , and a-bi are called what?

Answer 34

Complex Conjugates

Question 35

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

Answer 35

Fundamental Theorem of Algebra

Question 36

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

Answer 36

Linear Factorization Theorem

Question 37

Cannot be divided by any other number besides itself and 1., has no real zeros

Answer 37

Prime

Question 38

Prime, having no real zeros

Answer 38

Irreducible over the reals

Question 39

can be written in the form n(x)/d(x)

Answer 39

Rational Function

Question 40

x=a, as the function approaches infinity, or negative infinity

Answer 40

Vertical Asymptote

Question 41

y=b,as x approaches infinity or negative infinity

Answer 41

Horizontal Asymptote

Question 42

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..................

Answer 42

Slant of Oblique Asymptote