Graphing Absolute Value Functions

Hi guys! It's Fatima, your scribe for the day. Today, we learned about how to graph absolute value functions.


First of all, what is an absolute value? Well, an absolute value is a number's distance from zero. Hence, absolute values are always positive. Its mathematical definition is stated as follows:



Graphing absolute value functions is easy. Basically, the negative part of the graph on the y-axis should be flipped over the x-axis. There's no change in the past rules that we have first learned but note that they are to be applied in order. Here's an example:

Given the graph of y = f(x), graph the function y = -|f(x-1)|+2.

Here's how to do it step-by-step:




f(x)





First you move the graph one unit to the right as indicated by parameter B...
And then you reflect the negative part of the graph to show the effect of the
absolute value.

|f(x-1)|


Next, you reflect the whole graph over the x-axis because there's a negative sign in front of the function.

-|f(x-1)|


Lastly, you shift the graph up by 2 units.

-|f(x-1)|+2






And that's it! Sorry for taking so long for such a short post. Maybe there are some mistakes in my post so please feel free to comment because I was confused myself as I was doing this -___-

And oh, to grant her request, the next scribe will be emmelion :)