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This is a practice understanding of piecewise functions from an analytic viewpoint.
How You Can (And Should) Get More Practice!
Below is a few practice problems of various difficulty, but you will need considerably more practice than one each. For that reason
you should definitely use the green “Try Another” button in the top right corner at least two or three times to complete
additional versions of these questions for more practice. You should keep using that button until doing these problems feels straight
forward and easy, and then come back after a week or so of doing other stuff and try again to make sure it is still just as easy for
you.
Worked Out Examples Problem Videos
The following video may be helpful when trying to solve the problems in this practice section. Note that you may skip to the end
of the video to get completion credit for this page if you don’t need to watch them.
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Practice Problems
Theoretically Easier Difficulty Problem
To compute a piecewise function at a specific x-value, find the subdomain (on the right side of the definition) that contains the
x-value of interest.
Once you have identified the subdomain that contains the x-value, plug the x-value into the corresponding subfunction (the
function on the same row as the subdomain). There is no reason to plug in the x-value into any other subfunction.
Consider the following piecewise function:
Evaluate
Theoretically Medium Difficulty Problem
To compute a piecewise function at a specific x-value, find the subdomain (on the right side of the definition) that contains the
x-value of interest.
Once you have identified the subdomain that contains the x-value, plug the x-value into the corresponding subfunction (the
function on the same row as the subdomain). There is no reason to plug in the x-value into any other subfunction.
Consider the following piecewise function:
Evaluate
Theoretically Harder Difficulty Problem
To compute a piecewise function at a specific x-value, find the subdomain (on the right side of the definition) that contains the
x-value of interest.
Once you have identified the subdomain that contains the x-value, plug the x-value into the corresponding subfunction (the
function on the same row as the subdomain). There is no reason to plug in the x-value into any other subfunction.
Consider the following piecewise function:
Evaluate . If the answer does not exist, then enter DNE.
