Question

F(x)=x²-3x-2 is shifted 4 units right. The result is g(x). What is g(x)?

A. g(x) = (x+4)² - 3(x+4) - 2
B. g(x) = (x+4)² - 3x - 2
C. g(x)=x²-3x+2
D. g(x) = (x-4)² - 3(x-4) - 2

Answer 1

Answer: D g(x) =
`(X-4)^2-3(x-4)-2`

Explanation:
Translations have different types, there is vertical and horizontal translations, however as this equation is specifically regarding horizontal equations we will only look at horizontal translations. Horizontal translations occur inside the function and in this case the function is any x value. So we need to add the translation into any value of x. So we can see that choices A and D seems to be the only options as B misses one x and c is the same equation as before. Now Horizontal translations are flipped from common sense as you would think it would be A since right is positive on a number line but in this case and all translations on a horizontal axis that will send you to the left. So the translation we want would be (x-4)^2-3(x-4)-2 or D