math
posted by Kwena .
Why f(x) and g(x) do not cut the xaxis at the same number of points. Why h(x) does not cut the xaxis. Why do all cut the yaxis at one point only.

You probably have a graph of the three relations/functions in front of you, but we do not see it.
However, if f(x), g(x), and h(x) are functions, then the following statements are true:
1. Any defined function can intersect the xaxis any number of times, depending on the definition of the function. For example, the sine function cuts the xaxis infinite number of times.
2. By the definition of a function, any vertical line through any point on the domain of the function can intersect the function at exactly one point.
That is why the all the functions cut the yaxis at (at most) one point.