The fraction is underfined when the denominator is zero. Also, when the radical is negative. Thus, or . Thus, is the domain. But is always positive, because the leading coefficient is positive and its discrimanat is negative. Thus, this function is defined for all real numbers.Originally Posted byVigo

The horizontal tangents is when the derivative approaches infinity. Since is derivative is,Originally Posted byVigo

that happens when the denominator is zero. Thus, thus, but that never happens because we said that is always a positive number. Thus, it has no horizontal tangents.