Summarizing translations of the exponential function
Now that we have worked with each type of translation for the exponential function, we can summarize them in
[link] to arrive at the general equation for translating exponential functions.
Translations of the Parent Function
Translation
Form
Shift
Horizontally
units to the left
Vertically
units up
Stretch and Compress
Stretch if
Compression if
Reflect about the
x -axis
Reflect about the
y -axis
General equation for all translations
Translations of exponential functions
A translation of an exponential function has the form
Where the parent function,
is
shifted horizontally
units to the left.
stretched vertically by a factor of
if
compressed vertically by a factor of
if
shifted vertically
units.
reflected about the
x- axis when
Note the order of the shifts, transformations, and reflections follow the order of operations.
Writing a function from a description
Write the equation for the function described below. Give the horizontal asymptote, the domain, and the range.
is vertically stretched by a factor of
, reflected across the
y -axis, and then shifted up
units.
We want to find an equation of the general form
We use the description provided to find
and
We are given the parent function
so
The function is stretched by a factor of
, so
The function is reflected about the
y -axis. We replace
with
to get:
The graph is shifted vertically 4 units, so
Substituting in the general form we get,
The domain is
the range is
the horizontal asymptote is
General Form for the Translation of the Parent Function
Key concepts
The graph of the function
has a
y- intercept at
domain
range
and horizontal asymptote
See
[link] .
If
the function is increasing. The left tail of the graph will approach the asymptote
and the right tail will increase without bound.
If
the function is decreasing. The left tail of the graph will increase without bound, and the right tail will approach the asymptote
The equation
represents a vertical shift of the parent function
The equation
represents a horizontal shift of the parent function
See
[link] .
Approximate solutions of the equation
can be found using a graphing calculator. See
[link] .
The equation
where
represents a vertical stretch if
or compression if
of the parent function
See
[link] .
When the parent function
is multiplied by
the result,
is a reflection about the
x -axis. When the input is multiplied by
the result,
is a reflection about the
y -axis. See
[link] .
All translations of the exponential function can be summarized by the general equation
See
[link] .
Using the general equation
we can write the equation of a function given its description. See
[link] .
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
