SOLUTION: Find the domain of the function. If the domain can be specified by only one interval, use (NONE, NONE) for the second interval. f(x) = 5 / (x + 7) thank you for your help!

The expression on the right of

 

contains a denominator , which must
never = 0, so



or 



which means x must never equal -7, for there is a
vertical asymptote at   The graph is



It approaches but never touches the black asymptote drawn
below at x=-7:



Therefore it cannot have -7 in its domain, which is the
two intervals indicated on the x-axis below:



or on this number line, 

<=============================0====================================>
-15 -14 -13 -12 -11 -10  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2

which is the same thing as the x-axis on 
the graph above:

That is two intervals, and in interval notation is written:

       (-oo, -7) U (-7, oo)

Edwin