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?
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
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, . So, . Further, iff and iff . So, . Therefore, for 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.