is it still considered as discrete?
It is discrete because a bounce is considered from the time the ball leaves the ground until the time it touches the ground again. The table provides the maximum height reached between these two time events.
You know that something is discrete since you can easily count the number of times the ball hits the ground.
It is discrete because, correct, you can't have half a bounce. It doesn't make a difference if the "y" is considered "continuous". It's the x. "x" here, I assume, is the number of the bounce. Since you can't have half bounces, then it would be discrete.
When it comes to these tables and discrete or discontinuous, don't even bother considering the "y". Consider the "x". Can you take half of that? Here, no.
Can you specify "these kinds of problems"
This could be up to an individual's technical definition of discrete. Something like, "Is a square a rectangle?"
I consider discrete as in, for x and y, you "can" take find data points between what data points you have. For instance, if "x" were the months of the year, you can't find the month "March and a half" or "May and a half".
But, for something like bouncing balls, like in your example, you could find data points between 140 cm and 150 cm, for example, continuously forever. So, I would consider this continuous.
Some do consider, though, even though you "can" find data points between your data points, since you didn't find any of those points, the data would still be considered it discrete.
Can you specify "these kind of tables"