Sketching Absolute value graphs

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Homework Help Overview

The discussion revolves around sketching the graph of the function y = 2|x-1| - 3|x+1| + 3x + 1, which involves absolute value expressions and their behavior across different intervals of x.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss breaking the problem into intervals based on the absolute value expressions, specifically considering cases for x ≤ -1, -1 ≤ x ≤ 1, and x ≥ 1. There are questions about how to handle the absolute values in these intervals, including whether to make them negative or use a sign table.

Discussion Status

Participants are actively engaging with the problem, sharing their understanding of how to approach the absolute values in different intervals. Some guidance has been offered regarding handling the absolute values, but there is still uncertainty and a lack of consensus on the best method to apply.

Contextual Notes

There is mention of confusion due to multiple methods presented by the lecturer, which has led to participants seeking clarification on how to combine these approaches effectively.

w0lfed
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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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w0lfed said:
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
 
w0lfed said:
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
 
w0lfed said:
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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