Graph y=5-|3x+4|:
Note that `y=a|x-h|+k` is a transformation of the graph of y=|x| where:
a; is a vertical stretch/compression. If a<0 it is a reflection across the horizontal axis.
h: is a horizontal translation
k: is a vertical translation
So we rewrite in that form:
y=5-|3x+4|
`y=5-|3(x+4/3)|`
`y=-3|x+4/3|+5`
Thus we take the graph of y=|x|, reflect it across the x-axis, then move it 4/3 units left and 5 units up.
The graph of y=|x| is in black; the reflection in purple; the horizontal shift in blue; and the vertical shift in red which is the graph we seek: