Express the function f(x)=|6+8x| as a piecewise function

Question

Express the function f(x)=|6+8x| as a piecewise function

Answer 1

   the algebraic definition of the absolute value of x is

|x|  = { x, when x>=0

          {-x when x< 0

 

Translating this to your problem

 

when the expression within the absolute value is >=0 do nothing. when the expression within the absolute value is negative, multiply the expression by -1.

 

f(x) = { 6 + 8x, when 6+8x>=0

          { -6 - 8x, when 6+8x<0

 

6 + 8x >=0, 8x >= -6, x >= -3/4.......so you can rewrite this as

 

f(x) = { 6+8x, when x>= -3/4 

          { -6-8x, when x<-3/4