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.
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ma management ho
Amisha
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
belatari
Amisha
1st year ho
Amisha
nd u
Amisha
ahh
Amisha
kaha biratnagar
Amisha
ys
Amisha
kina k vo
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.