How does the graph of relate to its parent function?

The graph of a function can relate to its parent function through transformations such as translations, reflections, stretches, or compressions. For example, if the parent function is a quadratic ( f(x) = x^2 ), a transformed function like ( g(x) = (x - 2)^2 + 3 ) represents a horizontal shift to the right by 2 units and a vertical shift up by 3 units. These transformations affect the graph's position and shape while maintaining the overall characteristics of the parent function.