Check the picture below.
is it even? well, even functions use the y-axis as a mirror, so a pre-image on the right-side, will be a mirror of the image on the left-side, but in this case it isn't so, if you put a mirror right on the y-axis, the left-side will look a bit different.
does it have a zero at x = 0? well, just look at the graph, is the line touching the x-axis at 0? nope.
does it have an asymptote at 0? well, surely you can see it right there.
is it even? well, even functions use the y-axis as a mirror, so a pre-image on the right-side, will be a mirror of the image on the left-side, but in this case it isn't so, if you put a mirror right on the y-axis, the left-side will look a bit different.
does it have a zero at x = 0? well, just look at the graph, is the line touching the x-axis at 0? nope.
does it have an asymptote at 0? well, surely you can see it right there.