What is the domain and range of #y= ((x+1)(x-5)) /( x(x-5)(x+3))#?
Since this is a rational function, the domain will include undefined points on the graph called asymptotes.
Vertical asymptotes occur when the denominator is 0. Often, you will need to factor the denominator, but this has already been done.
Thus, you have your vertical asymptotes.
Your domain will be
The horizontal asymptotes of a rational function are obtained by comparing the degrees of the numerator and the denominator.
Multiplying everything out of factored form, we find that the degree of the numerator is 2 and that of the denominator is 3.
In a rational function of the form
Picking which scenario applies for our function, we realise there will be a vertical asymptote at
Thus, our range is
Hopefully this helps!