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To notice all transformations,we'll consider the parent function adn we'll identify it in the function g(x)=4(x+1)^2 - 3.
For the beginning, we'll expand the square from the expression of g(x):
g(x) = 4(x+1)^2 - 3
g(x) = 4(x^2 + 2x + 1) - 3
We'll remove the brackets:
g(x) = 4x^2 + 8x + 4 - 3
We'll combine like terms:
g(x) = 4x^2 + 8x + 1
We'll identify the parent function f(x) = x^2.
We'll apply square root both sides:
sqrt f(x) = sqrt x^2 = x
g(x) = 4f(x) + 8sqrt f(x) + 1
So, to get the function g(x), we'll follow the steps:
1) First, we'll multiply by 4, f(x):
2) We'll add square root of f(x), multiplied by 8:
4f(x) + 8sqrt f(x)
3) We'll add 1:
4f(x) + 8sqrt f(x) + 1
We've get the function g(x) = 4f(x) + 8sqrt f(x) + 1.
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