To simplify, let’s start by factoring out the inside of the function.
By factoring the inside, we can first horizontally stretch by 2, as indicated by the
on the inside of the function. Remember that twice the size of 0 is still 0, so the point (0,2) remains at (0,2) while the point (2,0) will stretch to (4,0). See
[link] .
Next, we horizontally shift left by 2 units, as indicated by
See
[link] .
Last, we vertically shift down by 3 to complete our sketch, as indicated by the
on the outside of the function. See
[link] .
A function can be shifted vertically by adding a constant to the output. See
[link] and
[link] .
A function can be shifted horizontally by adding a constant to the input. See
[link] ,
[link] , and
[link] .
Relating the shift to the context of a problem makes it possible to compare and interpret vertical and horizontal shifts. See
[link] .
Vertical and horizontal shifts are often combined. See
[link] and
[link] .
A vertical reflection reflects a graph about the
axis. A graph can be reflected vertically by multiplying the output by –1.
A horizontal reflection reflects a graph about the
axis. A graph can be reflected horizontally by multiplying the input by –1.
A graph can be reflected both vertically and horizontally. The order in which the reflections are applied does not affect the final graph. See
[link] .
A function presented in tabular form can also be reflected by multiplying the values in the input and output rows or columns accordingly. See
[link] .
A function presented as an equation can be reflected by applying transformations one at a time. See
[link] .
Even functions are symmetric about the
axis, whereas odd functions are symmetric about the origin.
Even functions satisfy the condition
Odd functions satisfy the condition
A function can be odd, even, or neither. See
[link] .
A function can be compressed or stretched vertically by multiplying the output by a constant. See
[link] ,
[link] , and
[link] .
A function can be compressed or stretched horizontally by multiplying the input by a constant. See
[link] ,
[link] , and
[link] .
The order in which different transformations are applied does affect the final function. Both vertical and horizontal transformations must be applied in the order given. However, a vertical transformation may be combined with a horizontal transformation in any order. See
[link] and
[link] .
Section exercises
Verbal
When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal shift from a vertical shift?
A horizontal shift results when a constant is added to or subtracted from the input. A vertical shifts results when a constant is added to or subtracted from the output.
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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