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
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
