transform an absolute value

**cubs3205** · May 28th 2007, 08:41 AM

The equation for this graph
is:
$ \frac {4\mid x + 1\mid(x +3 )(x - 1)^2}{(x + 1)^4(x - 3)} $

I am trying to get rid of the absolute value of (x+1) to form a rational function. But without the absolute value, the left third of the graph is flipped over the x-axis. Is there a way to make this same graph without the absolute value?

**Jhevon** · May 28th 2007, 08:43 AM

Originally Posted by cubs3205

The equation for this graph
is:
$ \frac {4\mid x + 1\mid(x +3 )(x - 1)^2}{(x + 1)^4(x - 3)} $

I am trying to get rid of the absolute value of (x+1) to form a rational function. But without the absolute value, the left third of the graph is flipped over the x-axis. Is there a way to make this same graph without the absolute value?

the $(x + 1)^4$ in the demominator is always positive, so you can cancel one of those with the $|x + 1|$ . so your graph will become: $\frac {4(x +3 )(x - 1)^2}{(x + 1)^3(x - 3)}$

**cubs3205** · May 28th 2007, 09:26 AM

yes I tried that but the left side is inverted. It is sloping up rather than sloping down like in the absolute value equation.

**Plato** · May 28th 2007, 09:30 AM

Yes you are correct. There is more to it.
$\frac{{\left( {4\left| {x + 1} \right|\left( {x + 3} \right)\left( {x - 1} \right)^2 } \right)}}{{\left( {x + 1} \right)^4 \left( {x - 3} \right)}} =$ $\left\{ {\begin{array}{lr} {\frac{{\left( { - 4\left( {x + 3} \right)\left( {x - 1} \right)^2 } \right)}}{{\left( {x + 1} \right)^3 \left( {x - 3} \right)}}} & {x < - 1} \\ {\frac{{\left( {4\left( {x + 3} \right)\left( {x - 1} \right)^2 } \right)}}{{\left( {x + 1} \right)^3 \left( {x - 3} \right)}}} & {x > - 1,\;x \not= 3} \\ \end{array}} \right.$

Thread: transform an absolute value

LinkBack

Thread Tools

Display

transform an absolute value

Similar Math Help Forum Discussions

Find the absolute maximum and absolute minimum values of f on the given interval.

finding absolute maximum and absolute minimum

Find the absolute maximum and absolute minimum values of the function

MAPLE: graph in hz, fourier transform, wavelet transform

Find the absolute maximum and absolute minimum

Search Tags