Let us consider a function y=f(x)
Here when x changes y will change. So y is dependant on x. x is the independent variable and y is dependent.
Since y is dependant there cannot be two y values for same x. Then it is not a function.
If a function intercept y axis that means in that point we have x=0. So there may be no intercepts with the y-axis. If that happens they same x will have two y values,so there is no function.
On the other hand for a y=f(x) function same y can have any number of x values. So a function can intercept x-axis any number of times.
The example graphs will show this clearly.
Just check how many times a single graph cuts y-axis and x-axis.
So a function can intercept x-axis any number of times depending on the function and y-axis can only intercept once as maximum.