Use calculus to determine the graph of the function. \[ f(x)=\frac{x^{2}-1}{x^{2}+3 x-4}\] Find the domain of \( f \).(Use symbolic notation and fractions where needed. Give your answers as intervals in the form (\(*,*\)). Use the symbol \(\infty \) for infinity, \( U \) for combining intervals, and an appropriate type of parenthesis "(",")","\([\)" or "\(]\)" depending on whether the interval is open or closed. Enter \(\varnothing \) if the interval is empty.) domain of \( f \) : Determine the \( x \)- and \( y \)-intercepts, if any. (Use symbolic notation and fractions where needed. Give your answer in the form of a comma-separated list of numbers. Enter DNE if the function has no \( y \)-intercept.)\[ x=\]\( y \) Find the horizontal and vertical asymptotes of \( f \).(Use symbolic notation and fractions where needed. Give your answers in the form of equations of the lines. If there are no asymptotes, enter DNE.) vertical asympotes: horizontal asympotes: Find the critical numbers of \( f \).(Use symbolic notation and fractions where needed. Give your answer in the form of a comma-separated list of numbers. Enter DNE if the function has no critical numbers.) critical numbers: Find the local maximum and minimum points of \( f \).(Use symbolic notation and fractions where needed. Give your answer in the form of a comma-separated list of point coordinates in the form (\(*,*\)). Enter DNE if the function has no local extremum.)