# Increasing & Decreasing of a function

• March 24th 2011, 06:07 AM
techdx69
Increasing & Decreasing of a function
Here's a quite simple question. But well, I've dropped outta school for about 3.5 years, now that I got back to school, I'd require to learn some basics before heading to advanced stuffs.

I'm kinda confused on the increasing and decreasing of a function when the function has an absolute value( |a| )

Eg. f(x)=| x-2 |

how do I differentiate them? Or what shall I do?

Thank you.

Tim
• March 24th 2011, 06:20 AM
Plato
Quote:

Originally Posted by techdx69
I'm kinda confused on the increasing and decreasing of a function when the function has an absolute value( |a| )
Eg. f(x)=| x-2 |how do I differentiate them? Or what shall I do?

Just plot the function. See where it is decreasing or increasing.
Do several of them to see a general pattern.
• March 24th 2011, 06:37 AM
techdx69
Sorry but unfortunately as I've mentioned its been a while since I've studied math and back then I do not acquired enough basics in math. And even if I do, I'd not remember any of em by now. And I do not remember how to sketch a graph. So if you don't mind, please teach me how to or give me a tutorial video with it. And its the "| |" absolute , thats bothering me in this question. :S
• March 24th 2011, 08:36 AM
emakarov
First, you can plot the graph of something like f(x) = |x - 2| by computing the value of f in several points, such as x = 0, 1, 2, 3, 4 and then connecting the dots.

Also, $|x|=
\begin{cases}
x, & x\ge 0\\
-x, & x < 0
\end{cases}$
. So, $|x - 2|=
\begin{cases}
x - 2, & x - 2\ge 0\\
-(x - 2), & x - 2 < 0
\end{cases}$
. Further, $x - 2\ge 0$ iff $x\ge 2$ and $x - 2 < 0$ iff $x < 2$. So, $|x - 2|=
\begin{cases}
x - 2, & x\ge 2\\
-(x - 2), & x < 2
\end{cases}$
. Therefore, for $x\ge 2$ you can draw the graph of x - 2. For x < 2, you need the graph of -(x - 2) = 2 - x. It can either be drawn directly, or you can use the fact that for any function g(x), the graph of -g(x) is obtained from the graph of g(x) by reflecting it with respect to the x-axis.