Section 5.2 Continuity: Incorrect interval of continuity for power functions #51
Description
See limitLawsAndContinuity/digInContinuity.tex
Section 5.2 Continuity: Incorrect interval of continuity for power functions
You give the incorrect interval of continuity for power function f(x) = x^b
The full description is of course messy:
If power b is a positive rational number in lowest terms with an odd denominator, then the domain of x^b is all real numbers
If power b is a positive rational number in lowest terms with an even denominator, then the domain of x^b is all nonnegative real numbers
If power b is a positive irrational number, then the domain of x^b is all nonnegative real numbers
You would not want to subject Business Calculus students to all that, but you need to say something that indicates that there is not one answer for all powers, and you want to not say something that is actually wrong.