I know how to use transformations of functions. The question is why do we need to learn transformations of functions? Also, how do we use them in real life, so as a real life application.
Transformations such as graphing y =(x-2)^2 + 1 using the graph of y =x^2.
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Transforming the graph can also be used "backwards" in the case of linear transformations, to keep the graph in place and shift/scale the axes, instead. For example (courtesy wikipedia), this is what allows the following chart to display both Celsius (bottom/left) and Fahrenheit (top/right) degrees.
I'm assuming a transformation of a function is like taking $f(x) = x^2$ as a base and then considering, for example $f(x) = ax^2 + c$. One example where this comes in handy to understand intuitively, that comes up in my job all the time, is in statistical modeling. Basically, when you want to fit a set of known data points to a function, it helps to understand how different transformations affect the output of the function, and how to interpret them.