What transformations change the graph of f(x) to the graph of g(x)? f(x) = x², g(x) = (x + 5)² - 9

Solution:

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. 

Hence, 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.

What transformations change the graph of f(x) to the graph of g(x)? f(x) = x², g(x) = (x + 5)² - 9

Summary:

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.