i have the function (x^3)/(2x^2-2)
how do I figure out if it's even or odd??
what are it's asymptotes(verticL or horizontal)??
The graph of this function has the same end behavior as the graph of _________??
thanks!
+129840 If this is even, then f(x) = f(-x)
f(x) = (x^3)/(2x^2-2) f(-x) = (-x)^3 / [ 2(-x)^2 - 2] = -x^3 / [ 2x^2 - 2] and these are not the same, so it's not even
If it's odd, then f(-x) = -f(x)
f(-x) = -x^3 / [ 2(-x)x^2 - 2] and -f(x) = -x^3 / [2x^2 - 2] and these are the same......so it's odd
The vertical asymptotes occur at the values that make the denominator 0, i.e., x = -1 and x = 1
There are no horizontal asymptotes......there is a "slant" asymptote of y = x/2
And this function has the same end behavior as y = x^3 / [2x^2] → y = x/2
Here's the graph : https://www.desmos.com/calculator/dgix5c99wx
