How do you write #y= abs(3x+6)# as a piecwise function?

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Answer 1 · 2017-08-02T21:45:07

See a solution process below:

Step 1) First, solve the term within the absolute value function for #0#:

#3x + 6 = 0#

#3x + 6 - color(red)(6) = 0 - color(red)(6)#

#3x + 0 = -6#

#3x = -6#

#(3x)/color(red)(3) = -6/color(red)(3)#

#(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = -2#

#x = -2#

Step 2) Multiply the term within the absolute value function by #-1# and write a "less than" inequality with the result of Step 1:

#-1(3x + 6) => -3x - 6#

#y = -3x - 6" for "x < -2#

Step 3) Take the term within the absolute value function and write a "greater than or equal to" inequality with the result of Step 1:

#y = 3x + 6" for "x >= -2#

Step 4) Combine Step 2 & Step 3 to form the piecewise function:

#y = {-3x - 6" for "x < -2; 3x + 6" for "x >= -2}#