Show a graph that represents: y= 5- |3x+4|.

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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...

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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:

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