How do you graph #y = -abs(x + 4)#?

1 Answer
Jul 5, 2015

Answer:

This is an upside-down V shape with arms having slope #+-1# and vertex at #(-4, 0)#

Explanation:

#abs(x+4) = x+4# when #x+4 >= 0#, that is when #x >= -4#
So #y = -abs(x+4) = -x-4# has slope #-1# when #x >= -4#

#abs(x+4) = -(x+4)# when #x+4 < 0#, that is when #x < -4#
So #y = -abs(x+4) = x+4# has slope #1# when #x < -4#

The vertex is at the point where #(x+4) = 0#, giving #x = -4# and #y = 0#. So the vertex is at #(-4, 0)#

The intersection with the #y# axis will be where #x=0#. Substituting #x=0# into the equation, we get #y = -abs(4) = -4#. So the intersection is at #(0, -4)#

graph{-abs(x+4) [-13.38, 6.62, -5.84, 4.16]}