I don´t know what I have to do!!!!!!

[michi1995]

I don´t know what I have to do!!!!!!

Hello,I have troubel with one exercise. I don´t know what I have to do.
I added the exercise in Appendix.
I do not have a pattern solution and in my math book there is no similar exercise.
Should I sketch something or should I calculate something I don´t know.

Maybe someone have a hint or a example for me how to solve this problem.

THX

 

[Cartesius24]

For each algebraic operation we can join geometrical one. For example
f(x-a)+b is translation of graph by vector [a,b] .

Read the same for affinity.

 

[Ishuda]

Hello,I have troubel with one exercise. I don´t know what I have to do.
I added the exercise in Appendix.
I do not have a pattern solution and in my math book there is no similar exercise.
Should I sketch something or should I calculate something I don´t know.

Maybe someone have a hint or a example for me how to solve this problem.

THX

Sometimes it is easier to talk about new variables rather than, for example, talking about two different x'. To do this we have
(x,y) -------->(u,v)
where, in this problem,
y = f(x),
u = (x-b)/a,
and
v = g(x) = c y + d.

So, how do we get u? Well first we we move x to the left by b [subtract b] then take that result and stretch (or shrink) it by 1/a. Note that you could have stretched (or shrank) x by 1/a then moved that result to the right by an amount of (-b/a) on the x scale.

How do we get v? Well that's the same procedure but with different constants.

As an example, let
y = f(x) = 3 x + 17
and describe
g(x) = 12 f[ (x+12)/2 ] - 3.
Well
u = [x - (-12)] / 2 = (x + 12) / 2
and
v = 12 y - 3.
So, we would stretch move x 12 to the right [add 12] and shrink that result by 0.5 to get u (the new x). To get v (the new y) we would stretch y by 12 and move that result down 3 [subtract 3] on the (old) y scale.