Quandaries
and Queries 

hi, my name is amber and i have talked to various tutors and teachers tonight on the internet and nobody can seem to answer my question. how do i begin to graph a piecewise function, absolute function or step function? this is an algebra II, 12 grade homework assignment. thank you. i appreciate your help. 

Hi Amber, Lets look at a particular example. Suppose that you have the piecewise function defined by
To begin to graph the function, divide the xaxis into three pieces.
Now, hopefully you know what the graphs the three expressions look like, f(x) = x, f(x) = 3 and f(x) = x. f(x) = x is a straight line through the origin with slope 1. But you only need the part of the graph with x < 1. Thus that piece of the graph is f(x) = 3 is a horizontal line, three units above the xaxis. I need this graph for x between 1 and 2. Thus adding this piece of the graph I get Finally f(x) = x is a straight line thtough the origin with slope 1. I need this for x larger than 2 and hence I get Thus the graph of the piecewise function is in blue above. Notice that the way the function is defined, f(1) = f(2) = 3 and hence I have put large dots at (1,3) and (2,3) to emphasize this. I hope this helps,


