-
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
Got questions? Get instant answers now!
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
Got questions? Get instant answers now!
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.
Got questions? Get instant answers now!
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
how to study physic and understand
what is conservative force with examples
Moses
the transfer of energy by a force that causes an object to be displaced; the product of the component of the force in the direction of the displacement and the magnitude of the displacement
AI-Robot
why is it from light to gravity
difference between model and theory
Esther
Is the ship moving at a constant velocity?
The full note of modern physics
introduction to applications of nuclear physics
the explanation is not in full details
I need more explanation or all about kinematics
Moses
I need more explanation or all about nuclear physics
aluet
Show that the equal masses particles emarge from collision at right angle by making explicit used of fact that momentum is a vector quantity
A wave is described by the function D(x,t)=(1.6cm) sin[(1.2cm^-1(x+6.8cm/st] what are:a.Amplitude b. wavelength c. wave number d. frequency e. period f. velocity of speed.
what is frontier of physics
A body is projected upward at an angle 45° 18minutes with the horizontal with an initial speed of 40km per second. In hoe many seconds will the body reach the ground then how far from the point of projection will it strike. At what angle will the horizontal will strike
Suppose hydrogen and oxygen are diffusing through air. A small amount of each is released simultaneously. How much time passes before the hydrogen is 1.00 s ahead of the oxygen? Such differences in arrival times are used as an analytical tool in gas chromatography.
what's the definition of physics
the science concerned with describing the interactions of energy, matter, space, and time; it is especially interested in what fundamental mechanisms underlie every phenomenon
AI-Robot
nuclei having the same Z and different N s
AI-Robot
Got questions? Join the online conversation and get instant answers!
Source:
OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.