# Absolute Values and piecewise functions

• Aug 26th 2008, 03:18 PM
Kingreaper
Absolute Values and piecewise functions
Rewrite the following into a piecewise function without any absolute values:

y = [tex]\mid x-3\mid+\mid5+x\mid[\math]

i don't know if i did latex right, so here it is in regular text

y=(absolute value x-3) + (absolute value 5+x)
• Aug 26th 2008, 03:50 PM
JaneBennet
Quote:

Originally Posted by Kingreaper
Rewrite the following into a piecewise function without any absolute values:

y = $\mid x-3\mid+\mid5+x\mid$

There are three “pieces” to the function:
• $x<-5$

• $-5\le x\le3$

• $x\ge3$

Consider each interval separately.
• Aug 26th 2008, 03:55 PM
Kingreaper
So how would I graph those?
• Aug 26th 2008, 04:01 PM
JaneBennet
Are you required to draw the graph as well? I thought you were only asked to rewrite the function without using absolute values.

Write the function in the form $y=\begin{cases}\ldots & x\le-5\\\\
\ldots & -5\le x\le 3\\\\
\ldots & x\ge3\end{cases}$
.
• Aug 26th 2008, 04:08 PM
Kingreaper
Quote:

Originally Posted by JaneBennet
Are you required to draw the graph as well? I thought you were only asked to rewrite the function without using absolute values.

Write the function in the form $y=\begin{cases}\ldots & x\le-5\\\\
\ldots & -5\le x\le 3\\\\
\ldots & x\ge3\end{cases}$
.

So for example, the first one, y = ... x less than or equal to -5. What would that look like in slope intercept form? usually it would have a number in front of the x's instead of those dots.
• Aug 26th 2008, 04:11 PM
Plato
Get your self a good graphing utility.
• Aug 26th 2008, 04:21 PM
Kingreaper
Thank you so much, but another problem has just come up that I have to do.

Solve the following:

$\sqrt{2x+1}+\sqrt{2x+6}=5$
• Aug 26th 2008, 04:34 PM
Soroban
Hello, Kingreaper!

Quote:

Solve: . $\sqrt{2x+1} + \sqrt{2x+6} \:=\:5$

Isolate a radical: . $\sqrt{2x+1} \;=\;5 - \sqrt{2x+6}$

Square both sides: . $\left(\sqrt{2x+1}\right)^2 \;=\;\left(5 - \sqrt{2x+6}\right)^2$

. . . . . . . . . . . . . . . . . $2x + 1 \;=\;25 - 10\sqrt{2x+6} + 2x + 6$

. . . . . . . . . . . . . . . $10\sqrt{2x+6} \:=\:30$

. . . . . . . . . . . . . . . . $\sqrt{2x+6} \:=\:3$

Square both sides: . $2x + 6 \:=\:9\quad\Rightarrow\quad 2x \:=\:3 \quad\Rightarrow\quad\boxed{ x \:=\:\frac{3}{2}}$

• Aug 26th 2008, 04:43 PM
Kingreaper
thank you all so much