Question

Describe the translation of the following function.

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

Answer 1

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

Answer 2

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