For each functon find the following (if they exist).
a. End Behavior including the equations of horizontal or slant asymptotes.
b. Vertical Asymptote(s). Distinguish between VA and Holes.
f(x)=−3x3x3−4x
For each functon find the following (if they exist).
a. End Behavior including the equations of horizontal or slant asymptotes.
b. Vertical Asymptote(s). Distinguish between VA and Holes.
y=−3x3x3−4xy=−3x3x(x−2)(x+2) sox≠±2,x≠0 y=−3x3x3−4x
y=−3x3÷x3(x3−4x)÷x3y=−31−4x2limx→0±y=−31−∞=0Hole at (0,0)limx→±∞y=−31−0=−3 Let δ be a miniscule positive number.limx→2+y=−31−(1−δ)=−3δ=−∞limx→−2−y=−31−(1−δ)=−3δ=−∞limx→2−y=−31−(1+δ)=−3−δ=∞limx→−2+y=−31−(1+δ)=−3−δ=∞
Hole at (0,0)
Vertical asymptotes at x=+2 and x=-2
Horizontal asymptotes at y=-3
Here is the graph