find the vertical asymptotes if any and the values of x corr

find the vertical asymptotes if any, and the values of x corresponding to holes if any, of the graph of each rational function.

I have done may of these but need this thoroughly explained so I can understand.

Solution

Asymptote is a line that the graph of a function approaches but never touches.

see in this function we know denominator can never be 0. so we will find out value of x for which denominator is 0 and eliminate that x from doman of y=f(x).

here denominator is x+7.

it cant be 0 .so x+7=0 gives x=-7. hence x=-7 is vertical asymptode of the function.