Final answer:
To determine the transformation of a parent function, we can rewrite the function and explain the shift horizontally or vertically compared to the original graph.
Step-by-step explanation:
To rewrite a function and determine its transformation, let's consider an example. Suppose we have the parent function f(x) = x^2. To shift the graph horizontally, we can add or subtract a value inside the parentheses of the function. For example, if we rewrite the function as f(x - 3) = (x - 3)^2, the graph will be shifted 3 units to the right compared to the parent function. If we rewrite the function as f(x + 2) = (x + 2)^2, the graph will be shifted 2 units to the left compared to the parent function.
To shift the graph vertically, we can add or subtract a value outside the parentheses. For example, if we rewrite the function as f(x) + 4 = x^2 + 4, the graph will be shifted 4 units up compared to the parent function. If we rewrite the function as f(x) - 2 = x^2 - 2, the graph will be shifted 2 units down compared to the parent function.