Both intercepts are 0.
sqrt(x^2+7) > 0 for all x, so there are no vertical asymptotes.
lim_(xrarroo)f(x) = lim_(xrarroo)x/(xsqrt(1+7/x^2)) = 1, so y=1 is a horizontal asymptote on the right.
lim_(xrarr-oo)f(x) = lim_(xrarr-oo)x/(-xsqrt(1+7/x^2)) = -1, so y = -1 is a horizontal asymptote on the left.
f'(x) = 7/(x^2+7)^(3/2) > 0 for all x, so there are no local extrema.
f''(x) = (-21x)/(x^2+7)^(5/2) changes sign at (0,0), so I have been taught that (0,0) is an inflection point. (Note that: f'(0) != 0, so some would say (0,0) is not an inflection point.)
graph{x/sqrt(x^2+7) [-16.01, 16.03, -7.95, 8.05]}
