This week I am writing about graphing absolute value functions. Something to always remember about absolute values is that they are always positive, this is very important to remember when graphing. Consider a table of values: a regular table of y=x can have negative and positive values, although when graphing an absolute value function ( y = |x| ) the points on the graph can never enter the quadrants where the y value will be negative.

So, when graphing a linear function with absolute values when the line on the graph reaches the x-intercept (or in this case, the critical point) the graph of the functions changes directions.

EX. y= |x-2|

So as we can see with the regular (y=x-2) the x-int is (2,0) so that is where our graph will change directions.

Now I will show an example from the assignment, the questions asks to complete the table of values, then graph the absolute value, find the intercepts, domain and range….

One more thing to remember when graphing absolute value functions is the piecewise notation. This is defined as being used to describe a function that has different definitions of subsets of the domain. What makes the most sense to me is to graph two separate functions:  the first one is the function inside the absolute value lines and the second one is the same function with a negative symbol outside the brackets. Here is an example I did of finding the piecewise notation from the same questions I included before.