How do you write #m(x) = |x+2| - 7# as a piecewise function?

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Answer 1 · 2017-04-28T14:47:21

Use the fact that #abs(u) = {(u,"if",u >= 0),(-u,"if",u < 0):}#

So

#m(x) = {((x+2)-7,"if",(x+2) >= 0),(-(x+2)-7,"if",(x+2) < 0):}#

We can simplify the expressions

#(x+2)-7 = x-5# and #-(x+2)-7 = -x-9#

and we can solve the inequalities

#(x+2) >= 0# is equivalent to #x >= -2# and
#(x+2) < 0# is equivalent to #x < -2#

So we can write the function:

#m(x) = {(x-5,"if",x >= -2),(-x-9,"if",x < -2):}#.