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