Question

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.

Answer 1

g (x) = 3lx+2l-8

Explanation:

Carlosego made a mistake on the horizontal shift.

y = f (x + c) shifts the graph c units to the left.

Therefore, g (x) = 3lx - 2 + 4l - 8 is

g (x) = 3lx+2l-8

Answer 2

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