To get from f(x) to -f(x+3)+2, we take this path:

f(x) to -f(x) to -f(x+3) to -f(x+3)+2

but we always must wait till last to add a number to the right side.

Graph of f(x) = |x|

    

To go from f(x) = |x| to -f(x) = -|x| we multiply by -1 and
that reflects the graph in the x-axis and we have this:

    

To go from -f(x) = -|x| to -f(x+3) = -|x+3| we shift the graph
left by 3 units and we have this:

    

To go from -f(x+3) = -|x| to -f(x+3)+2 = -|x+3|+2 we shift the graph
upward by 2 units and we have this:

    

Edwin

WE CAN ALSO REVERSE THE FIRST TWO STEPS IN THE ABOVE,
BUT WE MUST ALWAYS WAIT TILL LAST TO ADD TO OR SUBTRACT FROM
THE RIGHT SIDE, JUST AS IN "PEMDAS".  THAT IS, THE LAST 
OPERATION TO DO MUST ALWAYS BE TO SHIFT UP OR DOWN. 

To get from f(x) to -f(x+3)+2, You can also take this path

f(x) to f(x+3) to -f(x+3) to -f(x+3)+2

Graph of f(x) = |x|

    

To go from f(x) = |x| to f(x+3) = |x+3| we shift the graph
left by 3 units and we have this:

    

To go from f(x+3) = |x+3| to -f(x+3) = -|x+3| we multiply by -1 and
that reflects the graph in the x-axis and we have this:

    

To go from -f(x+3) = -|x| to -f(x+3)+2 = -|x+3|+2 we shift the graph
upward by 2 units and we have this:

    

Note that in doing it either way we MUST wait till last to shift
UP OR DOWN.

Edwin