Sketching Absolute value graphs

1. The problem statement, all variables and given/known data
I previously left some absolute value questions which contained a few simple equations and equalities.

i have a further question when it comes to slightly more complicated Absolute statements.

Sketch the graph of y = 2|x-1| - 3|x+1| + 3x + 1



2. Relevant equations
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3. The attempt at a solution
???
 

tiny-tim

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Sketch the graph of y = 2|x-1| - 3|x+1| + 3x + 1
Hi w0lfed! :smile:

Do it in three bits …

x ≤ -1, -1 ≤ x ≤ 1, x ≥ 1 :wink:
 
i think i need a lil more help...?
do we just make the absolute values negative for x=< - 1 or is there more to it like a sign table?
my lecturer just threw about 20 methods at us in 2 mins and i get quite confused because i try and combine em all and everyone says something else :S
 

tiny-tim

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do we just make the absolute values negative for x=< - 1 or is there more to it like a sign table?
eg for x = -7, |x + 1| = |-7 + 1| = |-6| = 6 …

and generally for x ≤ -1, |x + 1| = -(x + 1) :smile:
 
ok cool, i get that, but now do we make it positive or negative for -1 =< X =< 1

and then also...do we just leave and solve the values of X which are not absolute eg 3x like we would normally do

thanks very much Tiny Tim for you help
 

tiny-tim

Science Advisor
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ok cool, i get that, but now do we make it positive or negative for -1 =< X =< 1

and then also...do we just leave and solve the values of X which are not absolute eg 3x like we would normally do
Hi w0lfed! :smile:

look at each one separately … if it would be negative, multiply it by -1 …

and yes, leave the others like you normally would. :wink:
 

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