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.

Explanation:

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. 

Hence, 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.