f(x)=(x+8)^2 to the right 9 units

Question

determine the equation of g(x) that results from the function f(x)=(x+8)^2 to the right 9 units.

Answer 1

Moving a function to the right or left along the x-axis is known as a slide or translation.  The rules are:

1. f(x+a) moves f(x) "a" units to the left
2. f(x-a) moves f(x) "a" units to the right

 Your function is f(x) = (x+8)².  To move f(x) nine units to the right, apply rule 2 above; that is, you want g(x) = f(x-9)   To convert f(x) to f(x-9), simply replace the x in f(x) with (x-9):

 

g(x) = f(x-9) = ((x-9) + 8)² = (x-1)²