When transformations really happen?

I think that you like to read just about everything that is easily available “under the sun” therefore you may ask yourself questions regarding the transformation concept that we keep hearing just about everywhere.

Because I always wondered where this term of “transformation” comes from and why businesses and human resources are using it so often, I will try to show you how math is representing it.

When companies speak about an organic transformation what do they really imply?

In math there are functions that get transformed. We will consider horizontal translations, horizontal scaling, vertical translations and vertical scaling.

Starting with first which is horizontal translation, the domain is the set of all values that we can put in for x in the function without breaking the rule of algebra, such as division by 0 (i.e when nothing changes), or taking the logarithm of a negative number when there are abrupt changes (i.e. laying off).

If we translate by some positive real number, then our parabolas equation is changed "in the parentheses". When we say "in the parentheses" in this context we are referring to the notation: f(x) = x², and we will mean that we are changing the value in the parentheses.

We denote a horizontal translation as follows: y = (x-a)². As we can see, we add in the parentheses values that you translate the function on the horizontal axes. Horizontal scaling involves multiplying inside the parentheses by a nonzero constant. Horizontal scaling will happen when we multiply the x by a value.

The vertical translations and scaling affect the range of the function and it happens "outside" the parentheses. A vertical translation moves the graph vertically up or down depending on the value that our term “d” will take. In math we will always handle scaling first, then translations.

Now, as you may read between the lines, we always talk about translations therefore the question still remains as when a function transformation really happens? Well, the transformation happens when we have a combination of all of the above translations because at that point we have introduced enough variables and changes in the system such that we have a different set of values all together.

You might ask the question "why do we need transformations"? In fact we only need to ensure that positive results are observable and because there are no other ways to determine in which way the results can change, than we will translate the current functions.

But the main question remains as how do we know how the final transformation graph will look like? Because without knowing the final graph, how do we know how many translations will be required in order to get where we needed to be?

Another lesson will teach us more about the type of translations that are required to get us to positive results!


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