Example Question - quadratic function transformation

Transformation of Quadratic Function

The function g(x) is defined in terms of the function f(x) as follows: g(x) = 4[f(x) - 4]. Let's break down what this means for the graph of g(x) relative to the graph of f(x). The function f(x) = x^2 is the original quadratic function. Here's what happens step-by-step: 1. f(x) - 4: This operation translates the graph of f(x) vertically downward by 4 units. This moves every point on the graph of y = x^2 down 4 units on the y-axis. 2. 4[f(x) - 4]: This operation scales the graph of f(x) vertically by a factor of 4 after it has been shifted down by 4 units. Every y-coordinate of the points on the translated graph is multiplied by 4, stretching the graph away from the x-axis if y is positive and towards the x-axis if y is negative. Putting these two transformations together, we see that the original graph of f(x) is first shifted down by 4 units and then stretched vertically by a factor of 4. The correct answer is: D. The graph of g(x) is the graph of f(x) shifted down 4 units.transforms