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Mathematical Expression Editor
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This gives practice for understanding the absolute value analytically.
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.
Practice Problems
Theoretically Easier Difficulty Problem
Recall, to rewrite absolute values in a piece-wise format, you must find when the portion inside the absolute value is
non-negative, i.e. you need to set the portion inside to be greater than (or equal) to 0, then solve.
In this case, you want to set and then isolate . The result will tell you what values to use for the domain.
Once you have determined the domain, you can split the function into subfunctions for the piecewise form. Remember that, on
the domain where the inside was positive, you can replace the absolute value with parentheses. On the other segment you need to
multiply the inside by when you replace the absolute values with parentheses.
Consider the following absolute value expression:
Fill in the missing pieces of the following piecewise definition
Theoretically Medium Difficulty Problem
Recall, to rewrite absolute values in a piece-wise format, you must find when the portion inside the absolute value is
non-negative, i.e. you need to set the portion inside to be greater than (or equal) to 0, then solve.
In this case, you want to set and then isolate . The result will tell you what values to use for the domain.
Once you have determined the domain, you can split the function into subfunctions for the piecewise form. Remember that, on
the domain where the inside was positive, you can replace the absolute value with parentheses. On the other segment you need to
multiply the inside by when you replace the absolute values with parentheses.
Consider the following absolute value expression:
Fill in the missing pieces of the following piecewise definition
Theoretically Harder Difficulty Problem
Recall, to rewrite absolute values in a piece-wise format, you must find when the portion inside the absolute value is
non-negative, i.e. you need to set the portion inside to be greater than (or equal) to 0, then solve.
In this case, you want to set and then isolate . The result will tell you what values to use for the domain.
Once you have determined the domain, you can split the function into subfunctions for the piecewise form. Recall that, to find
the domain when you have a quadratic, you must use a sign chart to determine which -values correspond to positive values inside
the absolute value.
Remember that, on the domain where the inside was positive, you can replace the absolute value with parentheses. On the other
segment you need to multiply the inside by when you replace the absolute values with parentheses.
Consider the following absolute value expression:
Fill in the missing pieces of the following piecewise definition
Start typing the name of a mathematical function to automatically insert it.
(For example, "sqrt" for root, "mat" for matrix, or "defi" for definite integral.)
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Start typing the name of a mathematical function to automatically insert it.
(For example, "sqrt" for root, "mat" for matrix, or "defi" for definite integral.)