Sketching Absolute value graphs

[w0lfed]

Homework Statement

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

Homework Equations

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The Attempt at a Solution

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[tiny-tim]

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

Hi w0lfed!

Do it in three bits …

x ≤ -1, -1 ≤ x ≤ 1, x ≥ 1

 

[w0lfed]

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]

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)

 

[w0lfed]

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]

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!

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

and yes, leave the others like you normally would.