Question

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

Answer 1

c

Explanation:

if you shift to the right funnily enough, you have to "compensate" for that by SUBTRACTING the number of units.

EXTRA

To check, use a simple function f(x)= x²

The top of this parabola is at (0,0).

We want to check if g(x) = (x-4)² is the right function....

Now if f(x) is shifted 4 units right than all variables with x in them, need to be compensated for. The question is do you need to add or subtract...

We know that the result is g(x), and we know that the top of g(x) would end up at (4,0).

For that to happen you need to compensate with g(x) = (x-4)²

Now check if (4,0) is on g(x) by substituting x=4. if the result turns out to be 0, then you know it is ok...

Substituting x=4 indeed results to

4-4 = 0, so (4,0) is on g(x).

Conclusion, by checking this one special value, you now know you have found the correct compensation factor!

Answer 2

`\boxed{\mathrm{C.}\:\: g(x)=(x-4)^2-3(x-4)-2}`

Explanation:

The function is shifted 4 units right.

The value of x in the function is subtracted from 4, because this is a horizontal translation.

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

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