How do you find the transformation of a function?

For a function y = f(x), if a number is being added or subtracted inside the bracket then it is a horizontal translation. If the number is negative then the horizontal transformation is happening to the right side. If the number is positive then the horizontal transformation is happening to the left side.

Definitions

vertex –  is a point where two straight lines meet.

conjugate – A math conjugate is formed by changing the sign between two terms in a binomial. For instance, the conjugate of x + y is x – y.

maximum – a point at which a function’s value is greatest. If the value is greater than or equal to all other function values, it is an absolute maximum.

minimum – The smallest value of a set, function, etc.

domain – is the x values in a function such as f(x)

range – is the y values in a function such as y =.

Function Transformations. Transformation of functions means that the curve representing the graph either “moves to left/right/up/down” or “it expands or compresses” or “it reflects”. For example, the graph of the function f(x) = x² + 3 is obtained by just moving the graph of g(x) = x² by 3 units up.

We can tell this when looking at our equation:

 

Hope this helps 🙂