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

f(x) = x if x < -1

f(x) = 3 if -1 ≤ x ≤ 2

f(x) = -x if x > 2

To begin to graph the function, divide the x-axis into three pieces.

  1. everything less than -1
  2. everything between -1 and 2
  3. everything greater than 2

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 x-axis. 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,



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