Answered By Charles S

The function is classified as an absolute value quadratic function.  When a question asks to find the domain, you should always look at what 't' values are possible.  Quadratic functions don't have any restrictions on them ('t' can be anything). That's because when you are dealing with quadratic functions you are just squaring a number and you are allowed to square any number you want to.  So the domain is  $xER$xER in set notation or  $(-\infty,+\infty)$(−∞,+∞) in interval notation.   

Absolute value functions are kind of interesting in that they change any negative y values into positive y values.  Below is what the graph looks like. Notice that the graph does not go below the x axis so the range is  $y\ge0$y≥0 .  Note that this will not be the range for every absolute value graph and it could change if the graph was entirely above the x axis.