Describe the translation of the following function.

Y = - 1/3 |x + 4| - 2

Y equals negative one over three. absolute value of x plus 4. minus 2

Y=|x| is probably the original function

so we see

rewrite

y=-1/3 (|x+4|+6)

we see that the whole function was multiplied by - 1 and also by 1/3, so it is reflected across the x axis then vertically compressed by a factor of 1/3

see inside

|x+4|+6

to move up, a units, add a to whole function

this is 6, it was moved up 6 units

to move right, c units, subtract c from every x

so it was moved to the right - 4 units or 4 units to the left

so the transformation is

from y=|x| to y=-1/3|x+4|-2 is

move left 4 units

move up 6 units

compressed vertically by a factor of 1/3

reflected across x axis