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Mathematical Expression Editor
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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.
Theoretically Easier Difficulty Problem
To determine if a piecewise defined expression is a function, you need to know if it passes the vertical line
test.
You could graph the function, but the easier way is to check the domain definitions to see if they overlap.
If there is any overlap, and the functions aren’t the same function on that overlap, then it is not a function. If there is no overlap,
and each subfunction is a function, then the overall piecewise defined expression is a function.
Determine if the following piecewise definition is a function or not.
If the above piecewise definition is a function, enter . If it is not a function, then enter .
Theoretically Medium Difficulty Problem
To determine if a piecewise defined expression is a function, you need to know if it passes the vertical line
test.
You could graph the function, but the easier way is to check the domain definitions to see if they overlap.
If there is any overlap, and the functions aren’t the same function on that overlap, then it is not a function. If there is no overlap,
and each subfunction is a function, then the overall piecewise defined expression is a function.
Determine if the following piecewise definition is a function or not.
If the above piecewise definition is a function, enter . If it is not a function, then enter .
Theoretically Harder Difficulty Problem
To determine if a piecewise defined expression is a function, you need to know if it passes the vertical line
test.
You could graph the function, but the easier way is to check the domain definitions to see if they overlap.
If there is any overlap, and the functions aren’t the same function on that overlap, then it is not a function. If there is no overlap,
and each subfunction is a function, then the overall piecewise defined expression is a function.
Determine if the following piecewise definition is a function or not.
If the above piecewise definition is a function, enter . If it is not a function, then enter .
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.)