Question 631252
Are you asking how to graph/sketch the function?
A function like {{{f(x)=(x+4)(x-2)/8x}}} would have those zeros and those asymptotes. (There are many others).
The graph for {{{f(x)=(x+4)(x-2)/8x}}} looks like this:
{{{graph(300,300,-10,10,-5,5,(x^2+2x-8)/8x,(x+2)/8)}}} (The green line is the asymptote).
To sketch a function, I would start by graphing the zeros and the asymptotes.
(I would also graph any "holes" or "steps" where the function is not defined, but does not have a vertical asymptote).
Next, I would figure out where the function is positive and where it is negative.
Then, I would figure out where the function is increasing, and where it is decreasing. (If there is any local maximum and/or minimum, I would graph that point too.
Finally, I would sketch a smooth curve that goes through the graphed points, and gets closer and closer to the asymptotes as it heads out of the graph.