Question

F(x)=x^2-3x-2 is shifted 4 units right.the results is g(x). What is g(x)?

A. g(x)=x^2 -3x+2

B.g(x)=(x-4)^2-3x-(x-4)-2

C g(x)= (x+4)^2-3x-2

D g(x)= ( x+4)^2-3(x+4)-2

Answer 1

To shift the function `f(x) = x^2 - 3x - 2` 4 units to the right, we need to replace `x` with `(x - 4)` in the equation. This is because when we substitute `(x - 4)` for `x`, we are effectively shifting the entire graph 4 units to the right.

So, we get:

`g(x) = f(x-4) = (x-4)^2 - 3(x-4) - 2`

Expanding this equation, we get:

`g(x) = x^2 - 8x + 14`

Therefore, the answer is not among the options given. If we compare the answer choices to the actual equation, we find that option B is the closest match, but it still has some errors in the constant terms. Thus, the correct answer is not provided in the given options.