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 lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
