Verified Answer :

meerkat18

f(x) = (x+7)²
(x+7)(x+7) = x(x+7)+7(x+7) = x² + 7x + 7x + 49 = x² + 14x + 49

(x+9)² = (x+9)(x+9) = x(x+9)+9(x+9) = x² + 9x + 9x + 81 = x² + 18x + 81 
(x+5)² = (x+5)(x+5) = x(x+5)+5(x+5) = x² + 5x + 5x + 25 = x² + 10x + 25
(x-9)² = (x-9)(x-9) = x(x-9)-9(x-9) = x² - 9x - 9x + 81 = x² - 18x + 81
(x-5)² = (x-5)(x-5) = x(x-5)-5(x-5) = x² - 5x - 5x + 25 = x² - 10x + 25

I think g(x) based on the translation would be g(x) = (x+9)²

MrRoyal

The function that is based on the translation is g(x) = (x + 5)^2

How to determine the translation?

The function f(x) is given as:

f(x) = (x + 7)^2

The function f(x) is translated 2 units right to get function g(x)

This means that:

g(x) = f(x - 2)

So, we have:

f(x - 2) = (x -2 + 7)^2

Evaluate

f(x - 2) = (x + 5)^2

This gives

g(x) = (x + 5)^2

Hence, the function that is based on the translation is g(x) = (x + 5)^2

Read more about translation at:

https://brainly.com/question/8959437

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