Now that we have a feel for the set of values for which a logarithmic function is defined, we move on to graphing logarithmic functions. The family of logarithmic functions includes the parent function
along with all its transformations: shifts, stretches, compressions, and reflections.
We begin with the parent function
Because every logarithmic function of this form is the inverse of an exponential function with the form
their graphs will be reflections of each other across the line
To illustrate this, we can observe the relationship between the input and output values of
and its equivalent
in
[link].
Using the inputs and outputs from
[link] , we can build another table to observe the relationship between points on the graphs of the inverse functions
and
See
[link].
As we’d expect, the
x - and
y -coordinates are reversed for the inverse functions.
[link] shows the graph of
and
Observe the following from the graph:
has a
y -intercept at
and
has an
x - intercept at
The domain of
is the same as the range of
The range of
is the same as the domain of
Characteristics of the graph of the parent function,
f (
x ) = log
b (
x )
For any real number
and constant
we can see the following characteristics in the graph of
[link] shows how changing the base
in
can affect the graphs. Observe that the graphs compress vertically as the value of the base increases. (
Note: recall that the function
has base
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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