Unit 6: Alegbra II
horizontal line test
If every horizontal line intersects a graph of a function just once, then the function is one-to-one and therefore an inverse function exists.
vertical line test
If every vertical line intersects a graph just once, the graph is of a function.
The triangle of numbers used to find the pattern for any power of binomials is called ___ Triangle.
Pascal's
synthetic division
a shortcut method of dividing a polynomial by a linear polynomial by using only the coefficients of the terms of the polynomials
Pascal's Triangle
a triangular array of numbers such that each row is the coefficients of the terms of the expanded form of the powers of a binomial of the form (a+b)N
root of a polynomial
a value for the variable of a polynomial that makes the polynomial equal to zero
If the highest exponent of a polynomial function is odd, then the range of the function is ____ all real numbers.
always
The domain of a polynomial function is ____ all real numbers.
always
The set of polynomials is ___ closed under multiplication.
always
If the monomial is not zero, the product of a monomial and a polynomial will have ___ the polynomial.
as many terms as
In most cases, the product of a monomial and a binomial is a ___
binomial
In most cases, the product of a monomial and a binomial is a ___.
binomial
The coefficients of the terms on the right side of a ___ equation are the numbers in Pascal's Triangle.
binomial
The numerators of any rational roots of a polynomial will be factors of the ___.
constant term
Multiplying polynomials is done by applying the ___ Property when necessary.
distrubutive
To find the roots of a polynomial, it is often useful to find the ____ of the polynomial.
factors
The denominators of any rational roots of a polynomial will be factors of the ____.
leading coefficient
If the highest exponent of a polynomial function is even, then the range of the function is ____ all real numbers.
never
If the leading coefficient of a polynomial function is positive, then the right end of the graph ____ points down.
never
The set of polynomials is ___ closed under division
not
The set of polynomials is ___ closed under division.
not
A constant is a real ___.
number
A linear function, in the form f(x)=mx+b is a ___ function
polynomial
Closure means that whenever you add or subtract two polynomials, you get a ____.
polynomial
The composition of a polynomial function and another polynomial function will be a ___ function
polynomial
A term is a constant, a variable, or a ___ of numbers and variables.
product
Quotients of polynomials are called ___ expressions.
rational
A variable is a letter that stands for a(n) ___ number.
real
_____ number roots of a polynomial are the points where the graph of the related polynomial function crosses the x -axis
real
If the leading coefficient of a polynomial function is negative, then the left end of the graph ____ points down.
sometimes
The range of a polynomial function is ____ all real numbers
sometimes
Each number in Pascal's Triangle is the ___ of the two numbers directly above it in the previous row.
sum
A shortcut method of dividing a polynomial by a linear polynomial by using only the coefficients of the terms of the polynomial is called ___.
synthetic division
The value of a polynomial at x=1 is the remainder when the polynomial is divided by ____.
x-1
Roots of a polynomial are the values that make the polynomial equal to ___.
zero