Yes. For example, the domain and range of the cube root function are both the set of all real numbers.
Finding domains and ranges of the toolkit functions
We will now return to our set of toolkit functions to determine the domain and range of each.
For the
constant function
the domain consists of all real numbers; there are no restrictions on the input. The only output value is the constant
so the range is the set
that contains this single element. In interval notation, this is written as
the interval that both begins and ends with
For the
identity function
there is no restriction on
Both the domain and range are the set of all real numbers.For the
absolute value function
there is no restriction on
However, because absolute value is defined as a distance from 0, the output can only be greater than or equal to 0.For the
quadratic function
the domain is all real numbers since the horizontal extent of the graph is the whole real number line. Because the graph does not include any negative values for the range, the range is only nonnegative real numbers.For the
cubic function
the domain is all real numbers because the horizontal extent of the graph is the whole real number line. The same applies to the vertical extent of the graph, so the domain and range include all real numbers.For the
reciprocal function
we cannot divide by 0, so we must exclude 0 from the domain. Further, 1 divided by any value can never be 0, so the range also will not include 0. In set-builder notation, we could also write
the set of all real numbers that are not zero.For the
reciprocal squared function
we cannot divide by
so we must exclude
from the domain. There is also no
that can give an output of 0, so 0 is excluded from the range as well. Note that the output of this function is always positive due to the square in the denominator, so the range includes only positive numbers.For the
square root function
we cannot take the square root of a negative real number, so the domain must be 0 or greater. The range also excludes negative numbers because the square root of a positive number
is defined to be positive, even though the square of the negative number
also gives us
For the
cube root function
the domain and range include all real numbers. Note that there is no problem taking a cube root, or any odd-integer root, of a negative number, and the resulting output is negative (it is an odd function).
Given the formula for a function, determine the domain and range.
Exclude from the domain any input values that result in division by zero.
Exclude from the domain any input values that have nonreal (or undefined) number outputs.
Use the valid input values to determine the range of the output values.
Look at the function graph and table values to confirm the actual function behavior.
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
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