Given a tabular function, create a new row to represent a horizontal shift.
Identify the input row or column.
Determine the magnitude of the shift.
Add the shift to the value in each input cell.
Shifting a tabular function horizontally
A function
is given in
[link] . Create a table for the function
2
4
6
8
1
3
7
11
The formula
tells us that the output values of
are the same as the output value of
when the input value is 3 less than the original value. For example, we know that
To get the same output from the function
we will need an input value that is 3
larger . We input a value that is 3 larger for
because the function takes 3 away before evaluating the function
We continue with the other values to create
[link] .
5
7
9
11
2
4
6
8
1
3
7
11
1
3
7
11
The result is that the function
has been shifted to the right by 3. Notice the output values for
remain the same as the output values for
but the corresponding input values,
have shifted to the right by 3. Specifically, 2 shifted to 5, 4 shifted to 7, 6 shifted to 9, and 8 shifted to 11.
Identifying a horizontal shift of a toolkit function
[link] represents a transformation of the toolkit function
Relate this new function
to
and then find a formula for
Notice that the graph is identical in shape to the
function, but the
x- values are shifted to the right 2 units. The vertex used to be at (0,0), but now the vertex is at (2,0). The graph is the basic quadratic function shifted 2 units to the right, so
Notice how we must input the value
to get the output value
the
x -values must be 2 units larger because of the shift to the right by 2 units. We can then use the definition of the
function to write a formula for
by evaluating
The function
gives the number of gallons of gas required to drive
miles. Interpret
and
can be interpreted as adding 10 to the output, gallons. This is the gas required to drive
miles, plus another 10 gallons of gas. The graph would indicate a vertical shift.
can be interpreted as adding 10 to the input, miles. So this is the number of gallons of gas required to drive 10 miles more than
miles. The graph would indicate a horizontal shift.
Given the function
graph the original function
and the transformation
on the same axes. Is this a horizontal or a vertical shift? Which way is the graph shifted and by how many units?
The graphs of
and
are shown below. The transformation is a horizontal shift. The function is shifted to the left by 2 units.
Now that we have two transformations, we can combine them. Vertical shifts are outside changes that affect the output (
y -) values and shift the function up or down. Horizontal shifts are inside changes that affect the input (
x -) values and shift the function left or right. Combining the two types of shifts will cause the graph of a function to shift up or down
and left or right.
Questions & Answers
Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you.
Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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