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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: Stroodle on June 16, 2009, 06:44:03 pm

Title: Basic Absolute Value Graph
Post by: Stroodle on June 16, 2009, 06:44:03 pm: Can someone please show me how to graph $f(x)=-\lvert x+3\rvert+2$ using the same method as:
$f(x)=\rvert x-3\lvert+1=\left\{\begin{array}{cc}x-3+1,&\mbox{ if } x\geq 3\\3-x+1, & \mbox{ if } x<3\end{array}\right$
I'm just starting to learn these, and am not sure what to split the equation into.
Thanks for your help :)
Title: Re: Basic Absolute Value Graph
Post by: TrueTears on June 16, 2009, 06:46:47 pm: If $x+3 \ge 0$ then $f(x) = -(x+3)+2$

If x+3 < 0 then $f(x) = -(-(x+3)) + 2$

To solve you must have f(x) = 0

just solve that hybrid equation.

Sorry I didn't see your edit lol. Yea to sketch you can just sketch the 2 hybrid functions with domain restricted.
Title: Re: Basic Absolute Value Graph
Post by: Davoo! on June 16, 2009, 11:12:57 pm: Graph x+3 and for any part that goes over the positive side of the x-axis then reflect it into the negative (due to negative sign in front). Then just translate the whole thing up 2 units. Hope that helps =D
Title: Re: Basic Absolute Value Graph
Post by: Stroodle on June 17, 2009, 01:08:47 am: Cool. Thanks. I've got it now