What Transformations Change the Graph of f(x) to the graph of g(x)? f(x) = x2, g(x) = (x – 5)2 + 1.
We will be using the formula of transformations to solve this.
Answer: If f(x) = x2, g(x) = (x – 5)2 + 1, then the transformations from f(x) to g(x) is right 5 and up 1.
Let's solve this step by step.
Given that, f(x) = x2, g(x) = (x – 5)2 + 1.
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), we get h = 5 and k = 1.
⇒ We are shifting 5 to the right and 1 up.