(a)
stretches the graph of
vertically by a factor of
(b)
compresses the graph of
vertically by a factor of
Stretches and compressions of the parent function
f (
x ) =
bx
For any factor
the function
is stretched vertically by a factor of
if
is compressed vertically by a factor of
if
has a
y -intercept of
has a horizontal asymptote at
a range of
and a domain of
which are unchanged from the parent function.
Graphing the stretch of an exponential function
Sketch a graph of
State the domain, range, and asymptote.
Before graphing, identify the behavior and key points on the graph.
Since
is between zero and one, the left tail of the graph will increase without bound as
decreases, and the right tail will approach the
x -axis as
increases.
Since
the graph of
will be stretched by a factor of
In addition to shifting, compressing, and stretching a graph, we can also reflect it about the
x -axis or the
y -axis. When we multiply the parent function
by
we get a reflection about the
x -axis. When we multiply the input by
we get a
reflection about the
y -axis. For example, if we begin by graphing the parent function
we can then graph the two reflections alongside it. The reflection about the
x -axis,
is shown on the left side of
[link] , and the reflection about the
y -axis
is shown on the right side of
[link] .
(a)
reflects the graph of
about the x-axis. (b)
reflects the graph of
about the
y -axis.
Reflections of the parent function
f (
x ) =
bx
The function
reflects the parent function
about the
x -axis.
has a
y -intercept of
has a range of
has a horizontal asymptote at
and domain of
which are unchanged from the parent function.
The function
reflects the parent function
about the
y -axis.
has a
y -intercept of
a horizontal asymptote at
a range of
and a domain of
which are unchanged from the parent function.
Writing and graphing the reflection of an exponential function
Find and graph the equation for a function,
that reflects
about the
x -axis. State its domain, range, and asymptote.
Since we want to reflect the parent function
about the
x- axis, we multiply
by
to get,
Next we create a table of points as in
[link] .
Plot the
y- intercept,
along with two other points. We can use
and
Draw a smooth curve connecting the points:
The domain is
the range is
the horizontal asymptote is
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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.
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.
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