Concept and Vocab: Chapter 3 (thank you to those who contributed)

origin symmetry

(-x,-y)

False

T/F - A polynomial function with four sign changes must have four positive real zeros.

True

T/F-A polynomial function with one sign change must have one positive real zero.

n;1

The Linear Factorization Theorem states that an nth degree polynomial can be expressed as the product of a nonzero constant and ______ linear factors, where each linear factor has a coefficient _____

vertex

The turning point of a parabola

T/F: Odd-degree polynomial functions have graphs with opposite behavior at each end

true

x-axis symmetry (neither origin or even)

(-x,-y) Reflected across the x axis

The graph of a polynomial function of degree n​ has, at​ most, _________ turning points

(n-1)

If f is a polynomial function and​ f(a) and​ f(b) have opposite​ signs, then there must be at least one value of c between a and b for which ​f(c)equals=________. This result is called the __________ Theorem.

0, Intermediate Value

vertical asymptote

If the related rational expression of a function is written in simplest form and is undefined for x=a, then x=a is a vertical asymptote

a sub 0; a sub n

The Rational Zero Theorem states that if p/q is a rational zero of f​ (where p/q is reduced to lowest​ terms), then p is a factor of ___________ and q is a factor of _______________.

range

The _____ is the set of possible output values, which are shown on the y-axis.

end behavior

The behavior of the graph as x approaches positive infinity or negative infinity.

maximum

The largest value in the range of a function or data set.

T/F if the demoninator is nonnegative the domain is (- infinity, infinity)

True

Horizontal Asymptote

a horizontal line that the curve approaches but never reaches y=b

Descartes' Rule of Signs

a technique for finding the number of positive and negative roots to a polynomial equation with real coefficients

a-bi

if a+bi is a root of a polynomial equation with real​ coefficients, b≠0 then ______ is also a root of the equation.

Rational Zero Theorem

if f(x) = ax^n + ... +ax + a has integer coefficients, then every rational zero of f has the following form: p/q = factor of constant term / factor of leading coefficient

Linear Factorization Theorem

if f(x) is a polynomial of degree n where n>0, f has precisely n linear factors

axis of symmetry

parabolas are symmetric about a central line which is...

Smooth and continuous

polynomial functions are ___and___

quotients of polynomial functions

rational functions are....

Domain

the _____ of a graph consists of all the input values shown on the x-axis.

boundary points

the endpoints of an interval

a0 and an

Consider the polynomial function with integer coefficients. The Rational Zero Theorem states that if p/q is a rational zero of f (where p/q is reduced to lowest terms), then p is a factor of ___ and q is a factor of ____

Fundamental Theorem of Algebra

Every polynomial equation with degree greater than zero has at least one root in the set of complex numbers.

T/F THE GRAPH OF A POLYNOMIAL FUNCTION MAY HAVE A GAP OR BREAK

FALSE {SMOOTH AND CONTINUOUS}

n

If a polynomial equation is of degree​ n, then counting multiple roots​ separately, the equation has ___________ roots.

Asymptote

an imagianary line that can not be crossed

Parabola

any quadratic equation is called a

the behavior of the graph of a polynomial function to the far left or far right is called its

end behavior

even symmetry

f(-x)=f(x) (reflected on the y axis)

Reciprocal Function

f(x)=1/x

T/F: Some polynomial functions of degree 2 or higher have breaks in their graphs

false

test value

the numerical value obtained from a statistical test

minimum

the smallest possible amount of a function

symmetry

translation with even/odd/origin

T/F the coefficients of the variables in a polynomial function must be nonnegative integers

true

​T/F: Even-degree polynomial functions have graphs with the same behavior at each end

true

If r is a zero of even​ multiplicity, then the graph touches the​ x-axis and________. If r is a zero of odd​ multiplicity, then the graph___________the​ x-axis

turns around at r, crosses

a(x-h)^2+k

what is the standard formula

Every real zero of a polynomial function appears as​ a/an _________ of the graph

x-intercept