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- Precalculus
- 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.
Questions & Answers
Ayele, K., 2003. Introductory Economics, 3rd ed., Addis Ababa.
can you send the book attached ?
Ariel
the study of how humans make choices under conditions of scarcity
AI-Robot
U(x,y) = (x×y)1/2
find mu of x for y
U(x,y) = (xÃy)1/2
find mu of x for y
Desalegn
this is the study of how the society manages it's scarce resources
Belonwu
macroeconomic is the branch of economics which studies actions, scale, activities and behaviour of the aggregate economy as a whole.
husaini
difference between firm and industry
what's the difference between a firm and an industry
Abdul
firm is the unit which transform inputs to output where as industry contain combination of firms with similar production 😅😅
Abdulraufu
Suppose the demand function that a firm faces shifted from
Qd 120 3P
to
Qd 90 3P
and the supply function has shifted from
QS
20 2P
to
QS
10 2P .
a) Find the effect of this change on price and quantity.
b) Which of the changes in demand and supply is higher?
explain standard reason why economic is a science
factors influencing supply
scares
means__________________ends
resources. unlimited
Jan
economics is a science that studies human behaviour as a relationship b/w ends and scares means which have alternative uses
Jan
calculate the profit maximizing for demand and supply
Why qualify 28 supplies
Milan
out-of-pocket costs for a firm, for example, payments for wages and salaries, rent, or materials
AI-Robot
concepts of supply in microeconomics
identify a demand and a supply curve
there's a difference
Aryan
Demand curve shows that how supply and others conditions affect on demand of a particular thing and what percent demand increase whith increase of supply of goods
Israr
Hi Sir please how do u calculate Cross elastic demand and income elastic demand?
Abari
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Source:
OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
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