a) What is the domain of the function ?

(a) Think about what makes the fraction undefined. What value(s) of x makes the denominator 0?

(b) Notice that the function has a vertical asymptote. Substitute points around the vertical asymptote to find out if the range is $(-\infty,\infty)$, $(-\infty ,0)$,$(0,\infty)$,$[0,\infty)$, or $(-\infty ,0]$.

(c) Notice that the function has a vertical asymptote. Substitute points around the vertical asymptote to find out if the range is $(-\infty,\infty)$, $(-\infty ,0)$,$(0,\infty)$,$[0,\infty)$, or $(-\infty ,0]$​.

(b)         3x + 1

             ______

               x + 8

We  have     a   same degree polynomial  / same degree polynomial......this means that we will have a horizontal asymptote    at   y   =    ratio of  the coefficients on x  in the numerator/denominator  

So....the horizontal asymptote occurs  at     y  =  3 / 1  =  3

So...the range will be   (-infinity, 3)   and  (3, infinity )

Check the graph, here :   https://www.desmos.com/calculator/umaqjrwwtr

(c)         x^2

          ______

            1  -  x

Unfortunately....other than a graph, we will need to use some Calculus to find the range..this is a little involved, but not that difficult....hence.....the graph might be the best way to go :

https://www.desmos.com/calculator/vdr0itmcy5

The graph shows that the range is  (-inf, 4]   and [ 0, inf )