Question

F(x) = x² + 5x-1 is shifted 3 units right. The result is g(x). What is g(x)?

O A. g(x) = (x+3)² + 5x-1
OB. g(x)=x2 + 5x+2
C. g(x) = (x+3)2 +5(x + 3) - 1
D. g(x) = (x-3)2 + 5(x-3) -1

Answer 1

D

Explanation:

When a function is being shifted to the left, all x values will be added by y units shifted. (The constant that comes with x is excluded, eg. 3x shifted by 2 units left, becomes 3(x+2) and not 3x+2.)

Likewise, when a function is being shifted to the right, all x values will be subtracted by y units shifted. (Constant rules applies as well.)

Given f(x) is shifted 3 units right,

the new function, g(x) becomes:

`g(x) = {(x - 3)}^(2) + 5(x - 3) - 1`

Therefore the answer is D in this case.