Give me an example of transformation in maths work it as a mathematician

Answer 1

As a mathematician, one example of a transformation in math that I can discuss is the translation of a function.

Let's consider the function f(x) = x^2. A translation refers to shifting the graph of the function horizontally or vertically without changing its shape.

If we want to translate this function horizontally by 2 units to the right, we can achieve this by adding 2 to the input variable x. The transformed function would be g(x) = (x-2)^2.

Similarly, if we want to translate the function vertically by 3 units upwards, we can achieve this by adding 3 to the output variable f(x). The transformed function would be h(x) = x^2 + 3.

By using these transformations, we have effectively moved the graph of the original function f(x) to the right by 2 units in the case of g(x) and upwards by 3 units in the case of h(x). The shape of the parabola remains the same, but its position on the coordinate plane has shifted.