What Transformations Change the Graph of f(x) to the Graph of g(x)? f(x) = x2, g(x) = (x + 5)2 - 9
We will be using the formula of transformations to solve this.
Answer: If f(x) = x2, g(x) = (x + 5)2 - 9, then the transformations from f(x) to g(x) is 5 units to the left and 9 units down.
Let's solve this step by step.
Given that, f(x) = x2, g(x) = (x + 5)2 - 9
We have general formula of transformations as f(x) = a(bx − h)n + k
Here, k is the vertical shift, h is the horizontal shift, a is the vertical stretch and b is the horizontal stretch.
On comparing g(x) with the general formula of transformations, we get h = -5 and k = -9
⇒ The negative sign indicates that the graph has shifted 5 units to the left and 9 units down.