Function f, shown below, is translated down 3 units and left 4 units to create function g. f(x)=3|x-2|-5. Fill in the values of a, h, and k to write function g.
The graphs of the functions can be transformed, obtaining related functions. We consider two kinds of transformations. Vertical and horizontal displacements: It is assumed that c is a positive constant, ie c> 0 and y = f (x) then y = f (x) + c moves the graph c units up. y = f (x) - c moves the graph c units down. y = f (x + c) shifts the graph c units to the right. y = f (x - c) shifts the graph c units to the left. We have then: f (x) = 3 | x-2 | -5 Is down 3 units f (x) = 3 | x-2 | -5 -3 and left 4 units f (x) = 3 | (x-4) -2 | -5 -3 Rewriting g (x) = 3lx-6l-8 Answer: g (x) = 3lx-6l-8
