How do you solve and graph #abs(m-2)<8#?

1 Answer
Jun 13, 2017

Answer:

#f(m)={(m-10color(white)("xxx") {m:m>=2}),(-m-6color(white)("xxx") {m:m<2}):}#

for #dom f in (-oo,0)#

Explanation:

Recall that for a modulus function #f(x)=|x|#, #f(x)=x# for #x>=0# and #f(x)=-x# for #x<0#.

#|m-2| < 8#
#:. |m-2| - 8 < 0|#

If we call this a function

#f(m) = |m-2|-8# for #dom f in (-oo,0)#

then we can define it as a hybrid function, which follows the standard transformations of a function, we get:

#f(m)={((m-2)-8color(white)("xxx") {m:m>=2}),(-(m-2)-8color(white)("xxx") {m:m<2}):}#
#:. f(m)={(m-10color(white)("xxx") {m:m>=2}),(-m-6color(white)("xxx") {m:m<2}):}#

Of course, given the domain, we need only consider the function #g(m)=-m-6#, so to sketch, simply draw a straight line from the point #(0,-6)# remembering to leave an open circle at that coordinate.