Transformation of y= b*x into y = 5x + 3 will take place by vertical dilation by a scale factor of 5 and vertical translation of 3 units.
A parent function is the simplest form of a particular family of functions. A family of operations is a group of tasks with the same highest degree and therefore the same graph shape.
Function transformations "move" "resize" or "mirror" the graph of the parent function.
Mathematically speaking, the transformation of the function y = f(x) is usually y = a f(b(x + c)) + d. where a, b, c, and d are arbitrary real numbers representing transformations. Note that all outer numbers (outside the brackets) represent vertical translations, and all inner numbers represent horizontal translations. Addition and subtraction are translations, and multiplication and division are dilations. Every time a minus sign is multiplied it means it is a reflection here, 'a' stands for vertical stretch, 'b' stands for horizontal stretch, 'c' stands for horizontal movement, 'd' stands for vertical movement
We have given two functions y=b x and y = 5x + 3 which means that first, y changes into 5x i.e., vertical dilation by a scale factor of 5 and it changes to y = 5x + 3 i.e.., vertical translation of 3 units.
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