-
Home
- Algebra and trigonometry
- Polynomial and rational functions
- Graphs of polynomial functions
Key concepts
- Polynomial functions of degree 2 or more are smooth, continuous functions. See
[link] .
- To find the zeros of a polynomial function, if it can be factored, factor the function and set each factor equal to zero. See
[link]
,
[link]
, and
[link] .
- Another way to find the
intercepts of a polynomial function is to graph the function and identify the points at which the graph crosses the
axis. See
[link]
.
- The multiplicity of a zero determines how the graph behaves at the
intercepts. See
[link]
.
- The graph of a polynomial will cross the horizontal axis at a zero with odd multiplicity.
- The graph of a polynomial will touch the horizontal axis at a zero with even multiplicity.
- The end behavior of a polynomial function depends on the leading term.
- The graph of a polynomial function changes direction at its turning points.
- A polynomial function of degree
has at most
turning points. See
[link]
.
- To graph polynomial functions, find the zeros and their multiplicities, determine the end behavior, and ensure that the final graph has at most
turning points. See
[link] and
[link]
.
- Graphing a polynomial function helps to estimate local and global extremas. See
[link]
.
- The Intermediate Value Theorem tells us that if
have opposite signs, then there exists at least one value
between
and
for which
See
[link]
.
Section exercises
Verbal
What is the difference between an
intercept and a zero of a polynomial function
The
intercept is where the graph of the function crosses the
axis, and the zero of the function is the input value for which
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Explain how the Intermediate Value Theorem can assist us in finding a zero of a function.
If we evaluate the function at
and at
and the sign of the function value changes, then we know a zero exists between
and
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If the graph of a polynomial just touches the
x -axis and then changes direction, what can we conclude about the factored form of the polynomial?
There will be a factor raised to an even power.
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Algebraic
For the following exercises, find the
or
t -intercepts of the polynomial functions.
For the following exercises, use the Intermediate Value Theorem to confirm that the given polynomial has at least one zero within the given interval.
Questions & Answers
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evolutionary history and relationship of an organism or group of organisms
AI-Robot
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Abraham
HOW CAN MAN ORGAN FUNCTION
the diagram of the digestive system
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Ogenrwot
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
Genetics is the study of heredity
Misack
how does twins formed?
Misack
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
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DENG
cells is the basic structure and functions of all living things
Ramadan
is organisms that are similar into groups called tara
Yamosa
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Source:
OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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