Given the function
express the function as a polynomial in general form and determine the leading term, degree, and end behavior of the function.
The leading term is
so it is a degree 3 polynomial. As
approaches positive infinity,
increases without bound; as
approaches negative infinity,
decreases without bound.
Identifying local behavior of polynomial functions
In addition to the end behavior of polynomial functions, we are also interested in what happens in the “middle” of the function. In particular, we are interested in locations where graph behavior changes. A
turning point is a point at which the function values change from increasing to decreasing or decreasing to increasing.
We are also interested in the intercepts. As with all functions, the
y- intercept is the point at which the graph intersects the vertical axis. The point corresponds to the coordinate pair in which the input value is zero. Because a polynomial is a function, only one output value corresponds to each input value so there can be only one
y- intercept
The
x- intercepts occur at the input values that correspond to an output value of zero. It is possible to have more than one
x- intercept. See
[link].
Intercepts and turning points of polynomial functions
A
turning point of a graph is a point at which the graph changes direction from increasing to decreasing or decreasing to increasing. The
y- intercept is the point at which the function has an input value of zero. The
intercepts are the points at which the output value is zero.
Given a polynomial function, determine the intercepts.
Determine the
y- intercept by setting
and finding the corresponding output value.
Determine the
intercepts by solving for the input values that yield an output value of zero.
Determining the intercepts of a polynomial function
Given the polynomial function
written in factored form for your convenience, determine the
and
intercepts.
The
y- intercept occurs when the input is zero so substitute 0 for
The
y- intercept is (0, 8).
The
x -intercepts occur when the output is zero.
The
intercepts are
and
We can see these intercepts on the graph of the function shown in
[link] .
Astronomy (from Ancient Greek ἀστρονομία (astronomía) 'science that studies the laws of the stars') is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution.
Rafael
vjuvu
Elgoog
what is big bang theory?
Rosemary
what type of activity astronomer do?
Rosemary
No
Richard
the big bang theory is a theory which states that all matter was compressed together in one place the matter got so unstable it exploded releasing All its contents in the form of hydrogen
according to the theory of astronomers why the moon is always appear in an elliptical orbit?
Gatjuol
hi !!! I am new in astronomy....
I have so many questions in mind ....
all of scientists of the word they just give opinion only.
but they never think true or false ...
i respect all of them...
I believes whole universe depending
on true ...থিউরি
Govinda
hello
Jackson
hi
Elyana
we're all stars and galaxies a part of sun. how can science prove thx with respect old ancient times picture or books..or anything with respect to present time .but we r a part of that universe
there many theory to born universe but what is the reality of big bang theory to born universe
Asmit
what is the exact value of π?
Nagalakshmi
by big bang
universal
there are many theories regarding this it's on you believe any theory that you think is true ex. eternal inflation theory, oscillation model theory, multiple universe theory the big bang theory etc.
Aarya
I think after Big Bang!
Michele
from where on earth could u observe all the stars during the during the course of an year
is that so. the question was in the end of this chapter
Karuna
in theory, you could see them all from the equator (though over the course of a year, not at pne time). stars are measured in "declination", which is how far N or S of the equator (90* to -90*). Polaris is the North star, and is ALMOST 90* (+89*).
So it would just barely creep over the horizon.
Christopher
Got questions? Join the online conversation and get instant answers!