Michael J. answered • 03/12/16
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In order for a function to be continuous, the domain of the function must contain ALL real numbers. This means no cutoffs or vertical asymptotes. The domain is the set of x values in which a function is defined.
Our function is y= x3/2
If we rewrite this so that the function is in radical form, we get
y = √(x3)
Note that the value of x is being cubed first, then the result is being square-rooted. If we cube a negative number, the result will always be a negative number. However, we cannot take the square-root of a negative number because we end up with an imaginary number. This means that we cannot evaluate y for all negative values of x .
In conclusion, this function is not continuous.
Michael J.
Then in this case, the function is continuous when x≥0.
In my definition, I took into account an open interval of x. That will be (-∞, ∞). But you are right that functions can be continuous in a closed interval. Though, I believe the student might have received a more accurate answer if she gave a boundary condition.
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03/12/16
Raphael D.
03/12/16