Question

graph the rational function check for asymptotes, and symmetry(select the correct graph) if an anwer does not exist, enter DNE)
y=x/x^2+36
vertical asymptote x=___
horizontal asymptote: y=___
slant asymptote: y=_____
x-intercept: (x,y)=(___,___)
y-intercept:(x,y)=(___,___)

Answer 1

no vertical because
\[x^2+36\geq 0\] for all x

Answer 2

horizontal at y = 0 because degree of numerator is less than degree of denom

Answer 3

since there is a horizontal asymptote there is clearly no slant asymptote

Answer 4

x - intercept set numerator = 0 and solve

Answer 5

y - intercept replace x by 0 and see what you get