Originally Posted by

**DivideBy0** Is it possible to have a range of $\displaystyle \left[\frac{1}{4}, \infty\right]$ ?

I mean... you can't have something equal to infinity right, because there's always going to be something bigger... but I'm wondering if they did it like this because weird stuff happens at asymptotes.

This is the question that has it. I know how to do the question, but I don't know about my above question.

*A function with rule $\displaystyle f(x)=x^{-2}$ can be defined on different domains. In the list below, the first set represents the domain selected and the second set represents the corresponding range, but in one case the range is incorrect. Which pair does not have the correct range for the given domain?*

*A. Domain: $\displaystyle [-2,-1]$, Range: $\displaystyle \left[\frac{1}{4},1\right]$*

*B. Domain: $\displaystyle [-2,0) \cup (0,1]$, Range: $\displaystyle \left[\frac{1}{4}, \infty\right]$*

*C. Domain: $\displaystyle [-1,1] \setminus \lbrace{0\rbrace}$, Range: $\displaystyle [1,\infty)$*

*D. Domain: $\displaystyle [-1,2] \setminus \lbrace{0\rbrace}$, Range: $\displaystyle \left[\frac{1}{4},1\right]$*

*E. Domain: $\displaystyle [1,2)$, Range: $\displaystyle \left(\frac{1}{4},1\right]$*

*[1998 MM]*

Thanks