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- College algebra
- Polynomial and rational functions
- Power functions and polynomial
Key equations
general form of a polynomial function |
|
Key concepts
- A power function is a variable base raised to a number power. See
[link] .
- The behavior of a graph as the input decreases beyond bound and increases beyond bound is called the end behavior.
- The end behavior depends on whether the power is even or odd. See
[link] and
[link] .
- A polynomial function is the sum of terms, each of which consists of a transformed power function with positive whole number power. See
[link] .
- The degree of a polynomial function is the highest power of the variable that occurs in a polynomial. The term containing the highest power of the variable is called the leading term. The coefficient of the leading term is called the leading coefficient. See
[link] .
- The end behavior of a polynomial function is the same as the end behavior of the power function represented by the leading term of the function. See
[link] and
[link] .
- A polynomial of degree
will have at most
x- intercepts and at most
turning points. See
[link] ,
[link] ,
[link] ,
[link] , and
[link] .
Section exercises
Verbal
Explain the difference between the coefficient of a power function and its degree.
The coefficient of the power function is the real number that is multiplied by the variable raised to a power. The degree is the highest power appearing in the function.
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In general, explain the end behavior of a power function with odd degree if the leading coefficient is positive.
As
decreases without bound, so does
As
increases without bound, so does
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What can we conclude if, in general, the graph of a polynomial function exhibits the following end behavior? As
and as
The polynomial function is of even degree and leading coefficient is negative.
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Algebraic
For the following exercises, identify the function as a power function, a polynomial function, or neither.
For the following exercises, find the degree and leading coefficient for the given polynomial.
For the following exercises, determine the end behavior of the functions.
For the following exercises, find the intercepts of the functions.
Graphical
For the following exercises, determine the least possible degree of the polynomial function shown.
Questions & Answers
If c is the cost function for a particular product, find the marginal cost functions and their
values at x=10 a. c(x) = 800+ 0.04x + 0.0002x² b. c(x) = 250 + 100x + 0.001x²
how can I find set theory
how can I find set theory
Jarvis
is there an error on the one about the dime's thickness? says 2.2x10⁶=0.00135 m
hi, interested in algebra
how to reduce an equation?
Makan
by manipulation of both side
Al
9(y+8)-27 is 9y+45.
Why can't you reduce that to y+5? I know that's wrong but can't explain why
when you reduce an equation to its simplest terms, you can't change the value of the equation. reducing it to y + 5 is equivalent to dividing it by 9 which changes the value. you can multiply it by 1 or 9/9 which would give 9(y + 5). multiplying it by one does not change the value.
Philip
Given a polynomial expression, factor out the greatest common factor.
WHAT IS QUADRATIC EQUATION?
WHAT IS SYSTEM OF LINEAR INEWUALITIES?
Charles
WHAT IS SYSTEM OF LINEAR INEWUALITIES?
Charles
what are equations?
Charles
Definition of economics according to
karl Marx
Thomas malthus
Jeremy bentham
David Ricardo
J.K
Rakiya
Please help me is assignment
Rakiya
The 47th problem of Euclid
Kenneth
show that the set of all natural number form semi group under the composition of addition
what is the meaning
Dominic
explain and give four Example hyperbolic function
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the
fraction, the value of the fraction becomes 2/3. Find the original fraction.
2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
1. x + 6 2
-------------- = _
x + 9 + 6 3
x + 6 3
----------- x -- (cross multiply)
x + 15 2
3(x + 6) = 2(x + 15)
3x + 18 = 2x + 30 (-2x from both)
x + 18 = 30 (-18 from both)
x = 12
Test:
12 + 6 18 2
-------------- = --- = ---
12 + 9 + 6 27 3
Pawel
2.
(x) + (x + 2) = 60
2x + 2 = 60
2x = 58
x = 29
29, 30, & 31
Pawel
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
Q2
x+(x+2)+(x+4)=60
3x+6=60
3x+6-6=60-6
3x=54
3x/3=54/3
x=18
:. The numbers are 18,20 and 22
Naagmenkoma
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
Mark = x,. Don = 3x + 1
x + 3x + 1 = 113
4x = 112, x = 28
Mark = 28, Don = 85, 28 + 85 = 113
Pawel
how do I set up the problem?
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
please can go further on polynomials quadratic
Abdullahi
I need quadratic equation link to Alpa Beta
Source:
OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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