Reflect the graph of
(a) vertically and (b) horizontally.
Reflecting the graph vertically means that each output value will be reflected over the horizontal
t- axis as shown in
[link] .
Vertical reflection of the square root function
Because each output value is the opposite of the original output value, we can write
Notice that this is an outside change, or vertical shift, that affects the output
values, so the negative sign belongs outside of the function.
Reflecting horizontally means that each input value will be reflected over the vertical axis as shown in
[link] .
Horizontal reflection of the square root function
Because each input value is the opposite of the original input value, we can write
Notice that this is an inside change or horizontal change that affects the input values, so the negative sign is on the inside of the function.
Note that these transformations can affect the domain and range of the functions. While the original square root function has domain
and range
the vertical reflection gives the
function the range
and the horizontal reflection gives the
function the domain
Reflecting a tabular function horizontally and vertically
A function
is given as
[link] . Create a table for the functions below.
2
4
6
8
1
3
7
11
For
the negative sign outside the function indicates a vertical reflection, so the
x -values stay the same and each output value will be the opposite of the original output value. See
[link] .
2
4
6
8
–1
–3
–7
–11
For
the negative sign inside the function indicates a horizontal reflection, so each input value will be the opposite of the original input value and the
values stay the same as the
values. See
[link] .
A common model for learning has an equation similar to
where
is the percentage of mastery that can be achieved after
practice sessions. This is a transformation of the function
shown in
[link] . Sketch a graph of
This equation combines three transformations into one equation.
A horizontal reflection:
A vertical reflection:
A vertical shift:
We can sketch a graph by applying these transformations one at a time to the original function. Let us follow two points through each of the three transformations. We will choose the points (0, 1) and (1, 2).
First, we apply a horizontal reflection: (0, 1) (–1, 2).
Then, we apply a vertical reflection: (0, −1) (-1, –2).
Finally, we apply a vertical shift: (0, 0) (-1, -1).
This means that the original points, (0,1) and (1,2) become (0,0) and (-1,-1) after we apply the transformations.
In
[link] , the first graph results from a horizontal reflection. The second results from a vertical reflection. The third results from a vertical shift up 1 unit.
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
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