Describe the transformation of f represented by G . f(x)= 1/2x-1: g(x)= f(x-2)+7

Answer 1

f(x) = (1/2)x -1

g(x) = f(x-2) +7 is f(x) shifted right 2 and up 7

or

g(x)= (1/2)(x-2) -1 +7

= (1/2)x -1-1+7

= (1/2)x +5

g(x) = f(x) shifted up by 6 (5- -1 = 6)

take an easier example

y=x, shift it right by 2 is the same as shifted down by 2

it may help to draw a rough sketch

you can describe the transformation in different ways

f(x) = y=(1/2)x -1 is a line with slope =1/2, y intercept =-1

g(x)=y = (1/2)x +5 is a parallel line with same slope = 1/2, but y intercept = 5